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Mathematics LibreTexts

2.E: Foundation (exercises)

  • Page ID
    18072
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    Chapter Review Exercises

    Use a General Strategy to Solve Linear Equations

    Solve Equations Using the General Strategy for Solving Linear Equations

    In the following exercises, determine whether each number is a solution to the equation.

    \(10x−1=5x,x= \frac{1}{5}\)

    \(−12n+5=8n,n=−\frac{5}{4}\)

    Answer

    no

    In the following exercises, solve each linear equation.

    \(6(x+6)=24\)

    \(−(s+4)=18\)

    Answer

    \(s=−22\)

    \(23−3(y−7)=8\)

    \(\frac{1}{3}(6m+21)=m−7\)

    Answer

    \(m=−14\)

    \(4(3.5y+0.25)=365\)

    \(0.25(q−8)=0.1(q+7)\)

    Answer

    \(q=18\)

    \(8(r−2)=6(r+10)\)

    \(5+7(2−5x)=2(9x+1)−(13x−57)\)

    Answer

    \(x=−1\)

    \((9n+5)−(3n−7)=20−(4n−2)\)

    \(2[−16+5(8k−6)]=8(3−4k)−32\)

    Answer

    \(k=\frac{3}{4}\)

    Classify Equations

    In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.

    \(17y−3(4−2y)=11(y−1)+12y−1\)

    \(9u+32=15(u−4)−3(2u+21)\)

    Answer

    \(contradiction; no solution\)

    \(−8(7m+4)=−6(8m+9)\)

    Solve Equations with Fraction or Decimal Coefficients

    In the following exercises, solve each equation.

    \(\frac{2}{5}n−\frac{1}{10}=\frac{7}{10}\)

    Answer

    \(n=2\)

    \(\frac{3}{4}a−\frac{1}{3}=\frac{1}{2}a+\frac{5}{6}\)

    \(\frac{1}{2}(k+3)=\frac{1}{3}(k+16)\)

    Answer

    \(k=23\)

    \(\frac{5y−1}{3}+4=\frac{-8y+4}{6}\)

    \(0.8x−0.3=0.7x+0.2\)

    Answer

    \(x=5\)

    \(0.10d+0.05(d−4)=2.05\)

    Use a Problem-Solving Strategy

    Use a Problem Solving Strategy for Word Problems

    In the following exercises, solve using the problem solving strategy for word problems.

    Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?

    Answer

    There are 116 people.

    There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.

    Solve Number Word Problems

    In the following exercises, solve each number word problem.

    The sum of a number and three is forty-one. Find the number.

    Answer

    38

    One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.

    One number is two more than four times another. Their sum is negative thirteen. Find the numbers.

    Answer

    \(−3,−10\)

    The sum of two consecutive integers is \(−135\). Find the numbers.

    Find three consecutive even integers whose sum is 234.

    Answer

    76, 78, 80

    Find three consecutive odd integers whose sum is 51.

    Koji has $5,502 in his savings account. This is $30 less than six times the amount in his checking account. How much money does Koji have in his checking account?

    Answer

    $922

    Solve Percent Applications

    In the following exercises, translate and solve.

    What number is 67% of 250?

    12.5% of what number is 20?

    Answer

    \(160\)

    What percent of 125 is 150?

    In the following exercises, solve.

    The bill for Dino’s lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?

    Answer

    \($3.89\)

    Dolores bought a crib on sale for $350. The sale price was 40% of the original price. What was the original price of the crib?

    Jaden earns $2,680 per month. He pays $938 a month for rent. What percent of his monthly pay goes to rent?

    Answer

    \(35%\)

    Angel received a raise in his annual salary from $55,400 to $56,785. Find the percent change.

    Rowena’s monthly gasoline bill dropped from $83.75 last month to $56.95 this month. Find the percent change.

    Answer

    \(32%\)

    Emmett bought a pair of shoes on sale at 40% off from an original price of $138. Find ⓐ the amount of discount and ⓑthe sale price.

    Lacey bought a pair of boots on sale for $95. The original price of the boots was $200. Find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent, if needed.)

    Answer

    ⓐ \($105\) ⓑ \(52.5%\)

    Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350% mark-up. Find ⓐthe amount of the mark-up and ⓑ the list price.

    Solve Simple Interest Applications

    In the following exercises, solve.

    Winston deposited $3,294 in a bank account with interest rate 2.6% How much interest was earned in five years?

    Answer

    \($428.22\)

    Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the $4,500 plus $243 interest. What was the rate of interest?

    Jaime’s refrigerator loan statement said he would pay $1,026 in interest for a four-year loan at 13.5%. How much did Jaime borrow to buy the refrigerator?

    Answer

    \($1,900\)

    Solve a formula for a Specific Variable

    Solve a Formula for a Specific Variable

    In the following exercises, solve the formula for the specified variable.

    Solve the formula
    \(V=LWH\) for L.

    Solve the formula
    \(A=\frac{1}{2}d_1d_2\) for \(d_2\).

    Answer

    \(d_2=\frac{2A}{d_1}\)

    Solve the formula
    \(h=48t+\frac{1}{2}at^2\) for t.

    Solve the formula
    4x−3y=12 for y.

    Answer

    \(y=\frac{4x}{3}−4\)

    Use Formulas to Solve Geometry Applications

    In the following exercises, solve using a geometry formula.

    What is the height of a triangle with area 67.567.5 square meters and base 9 meters?

    The measure of the smallest angle in a right triangle is 45°45° less than the measure of the next larger angle. Find the measures of all three angles.

    Answer

    \(22.5°,67.5°,90°\)

    The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.

    Find the length of the hypotenuse.

    The figure is a right triangle with a base of 10 units and a height of 24 units.

    Answer

    \(26\)

    Find the length of the missing side. Round to the nearest tenth, if necessary.

    The figure is a right triangle with a height of 15 units and a hypotenuse of 17 units.

    Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is eight feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire? Approximate to the nearest tenth, if necessary.

    The figure is a right triangle with a height of 8 feet and a hypotenuse of 10 feet.

    Answer

    6 feet 

    Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

    The figure illustrates rectangular shelving whose width of 36 inch and height of 15 inches forms a right triangle with a diagonal brace.

    The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.

    Answer

    \(24.5\) cm, \(12.5\) cm

    The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.

    The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.

    Answer

    9 ft, 14 ft, 12 ft

    Solve Mixture and Uniform Motion Applications

    Solve Coin Word Problems

    In the following exercises, solve.

    Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. How many of each does she have?

    Lenny has $3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?

    Answer

    nine pennies, six dimes, 12 quarters

    Solve Ticket and Stamp Word Problems

    In the following exercises, solve each ticket or stamp word problem.

    Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was three less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?

    125 tickets were sold for the jazz band concert for a total of $1,022. Student tickets cost $6 each and general admission tickets cost $10 each. How many of each kind of ticket were sold?

    Answer

    57 students, 68 adults

    Yumi spent $34.15 buying stamps. The number of $0.56 stamps she bought was 10 less than four times the number of $0.41 stamps. How many of each did she buy?

    Solve Mixture Word Problems

    In the following exercises, solve. 

    Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?

    Answer

    \(2.2\) lbs of raisins, \(7.8\) lbs of nuts

    Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?

    Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)

    Answer

    \(9.7%\)

    Solve Uniform Motion Applications

    In the following exercises, solve.

    When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa two hours to drive the same distance. Elsa’s speed is seven miles per hour faster than Gabe’s speed. Find Gabe’s speed and Elsa’s speed.

    Louellen and Tracy met at a restaurant on the road between Chicago and Nashville. Louellen had left Chicago and drove 3.2 hours towards Nashville. Tracy had left Nashville and drove 4 hours towards Chicago, at a speed one mile per hour faster than Louellen’s speed. The distance between Chicago and Nashville is 472 miles. Find Louellen’s speed and Tracy’s speed.

    Answer

    Louellen 65 mph, Tracy 66 mph

    Two busses leave Amarillo at the same time. The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour. How many hours will it take them to be 375 miles apart?

    Kyle rowed his boat upstream for 50 minutes. It took him 30 minutes to row back downstream. His speed going upstream is two miles per hour slower than his speed going downstream. Find Kyle’s upstream and downstream speeds.

    Answer

    upstream 3 mph, downstream 5 mph

    At 6:30, Devon left her house and rode her bike on the flat road until 7:30. Then she started riding uphill and rode until 8:00. She rode a total of 15 miles. Her speed on the flat road was three miles per hour faster than her speed going uphill. Find Devon’s speed on the flat road and riding uphill.

    Anthony drove from New York City to Baltimore, which is a distance of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was light for the rest of the drive, and he arrived at 7:30. His speed in light traffic was four miles per hour more than twice his speed in heavy traffic. Find Anthony’s driving speed in heavy traffic and light traffic.

    Answer

    heavy traffic 32 mph, light traffic 66 mph

    Solve Linear Inequalities

    Graph Inequalities on the Number Line

    In the following exercises, graph the inequality on the number line and write in interval notation.

    \(x<−1\)

    \(x\geq −2.5\)

    Answer

    The solution is x is greater than or equal to negative 2.5. The number line shows a left bracket at negative 2.5 with shading to its right. The interval notation is negative 2.5 to infinity within a bracket and a parenthesis.

    \(x\leq \frac{5}{4}\)

    \(x>2\)

    Answer

    The solution is x is greater than 2. The number line shows a left parenthesis at 2 with shading to its right. The interval notation is 2 to infinity within parentheses.

    \(−2<x<0\)

    \(-5\leq x<−3\)

    Answer

    The solution is negative 5 is less than or equal to x which is less than negative 3. The number line shows a closed circle at negative 5, an open circle at negative 3, and shading between the circles. The interval notation is negative 5 to negative 3 within a bracket and a parenthesis.

    \(0\leq x\leq 3.5\)

    Solve Linear Inequalities

    In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 

    \(n−12\leq 23\)

    Answer

    The solution is n is less than or equal to 35. The number line shows a a right bracket at 35 with shading to its left. The interval notation is negative infinity to 35 within a parenthesis and a bracket.

    \(a+\frac{2}{3}\geq \frac{7}{12}\)

    \(9x>54\)

    Answer

    The solution is x is greater than 6. The number line shows a left parenthesis at 6 with shading to its right. The interval notation is 6 to infinity within parentheses.

    \(\frac{q}{−2}\geq −24\)

    \(6p>15p−30\)

    Answer

    The solution is p is less than ten-thirds. The number line shows a right parenthesis at ten-thirds with shading to its left. The interval notation is negative infinity to ten-thirds within parentheses.

    \(9h−7(h−1)\leq 4h−23\)

    \(5n−15(4−n)<10(n−6)+10n\)

    Answer

    The solution is an identity. Its solution on the number line is shaded for all values. The solution in interval notation is negative infinity to infinity within parentheses.

    \(\frac{3}{8}a−\frac{1}{12}a>\frac{5}{12}a+\frac{3}{4}\)

    Translate Words to an Inequality and Solve

    In the following exercises, translate and solve. Then write the solution in interval notation and graph on the number line.

    Five more than z is at most 19. 

    Answer

    The inequality is z plus 5 is less than or equal to 19. Its solution is z is less than or equal to 14. The number line shows a right bracket at 14 with shading to its left. The interval notation is negative infinity to 14 within a parenthesis and a bracket.

    Three less than c is at least 360.

    Nine times n exceeds 42.

    Answer

    The inequality is 9 n is greater than 42. Its solution is n is greater than fourteen-thirds. The number line shows a left parentheses at fourteen-thirds with shading to its right. The interval notation is fourteen-thirds to infinity within parentheses.

    Negative two times a is no more than eight.

    Solve Applications with Linear Inequalities

    In the following exercises, solve.

    Julianne has a weekly food budget of $231 for her family. If she plans to budget the same amount for each of the seven days of the week, what is the maximum amount she can spend on food each day?

    Answer

    $33 per day

    Rogelio paints watercolors. He got a $100 gift card to the art supply store and wants to use it to buy 12″ × 16″ canvases. Each canvas costs $10.99. What is the maximum number of canvases he can buy with his gift card?

    Briana has been offered a sales job in another city. The offer was for $42,500 plus 8% of her total sales. In order to make it worth the move, Briana needs to have an annual salary of at least $66,500. What would her total sales need to be for her to move?

    Answer

    at least $300,000

    Renee’s car costs her $195 per month plus $0.09 per mile. How many miles can Renee drive so that her monthly car expenses are no more than $250?

    Costa is an accountant. During tax season, he charges $125 to do a simple tax return. His expenses for buying software, renting an office, and advertising are $6,000. How many tax returns must he do if he wants to make a profit of at least $8,000?

    Answer

    at least 112 jobs

    Jenna is planning a five-day resort vacation with three of her friends. It will cost her $279 for airfare, $300 for food and entertainment, and $65 per day for her share of the hotel. She has $550 saved towards her vacation and can earn $25 per hour as an assistant in her uncle’s photography studio. How many hours must she work in order to have enough money for her vacation?

    Solve Compound Inequalities

    Solve Compound Inequalities with “and”

    In each of the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.

    \(x\leq 5\) and \(x>−3\)

    Answer

    The solution is negative 3 is less than x which is less than or equal to 5. The number line shows an open circle at negative 3 and a closed circle at 5. The interval notation is negative 3 to 5 within a parenthesis and a bracket.

    \(4x−2\leq 4\) and
    \(7x−1>−8\)

    \(5(3x−2)\leq 5\) and
    \(4(x+2)<3\)

    Answer

    The solution is negative x is less than negative five-fourths. The number line shows an open circle at negative five-fourths with shading to its left. The interval notation is negative infinity to negative five-fourths within parentheses.

    \(34(x−8)\leq 3\) and
    \(15(x−5)\leq 3\)

    \(34x−5\geq −2\) and
    \(−3(x+1)\geq 6\)

    Answer

    The solution is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation

    \(−5\leq 4x−1<7\)

    Solve Compound Inequalities with “or”

    In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

    \(5−2x\leq −1\) or
    \(6+3x\leq 4\)

    Answer

    The solution is x is less than negative two-thirds or x is greater than or equal to 3. The number line shows a closed circle at negative two-thirds with shading to its left and a closed circle at 3 with shading to its right. The interval notation is the union of negative infinity to negative two-thirds within a parenthesis and a bracket and 3 to infinity within a bracket and a parenthesis.

    \(3(2x−3)<−5\) or
    \(4x−1>3\)

    \(34x−2>4\) or \(4(2−x)>0\)

    Answer

    The solution is x is less than 2 or x is greater than 8. The number line shows an open circle at 2 with shading to its left and an open circle at 8 with shading to its right. The interval notation is the union of negative infinity to 8 within parentheses and 8 to infinity within parentheses.

    \(2(x+3)\geq 0\) or
    \(3(x+4)\leq 6\)

    \(12x−3\leq 4\) or
    \(13(x−6)\geq −2\)

    Answer

    The solution is an identity. Its solution on the number line is shaded for all values. The solution in interval notation is negative infinity to infinity within parentheses.

    Solve Applications with Compound Inequalities

    In the following exercises, solve. 

    Liam is playing a number game with his sister Audry. Liam is thinking of a number and wants Audry to guess it. Five more than three times her number is between 2 and 32. Write a compound inequality that shows the range of numbers that Liam might be thinking of.

    Elouise is creating a rectangular garden in her back yard. The length of the garden is 12 feet. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Use a compound inequality to find the range of values for the width of the garden.

    Answer

    \(6\leq w\leq 12\)

    Solve Absolute Value Inequalities

    Solve Absolute Value Equations

    In the following exercises, solve.

    \(|x|=8\)

    \(|y|=−14\)

    Answer

    no solution

    \(|z|=0\)

    \(|3x−4|+5=7\)

    Answer

    \(x=2,x=\frac{2}{3}\)

    \(4|x−1|+2=10\)

    \(−2|x−3|+8=−4\)

    Answer

    \(x=9,x=−3\)

    \(|12x+5|+4=1\)

    \(|6x−5|=|2x+3|\)

    Answer

    \(x=2,x=14\)

    Solve Absolute Value Inequalities with “less than”

    In the following exercises, solve each inequality. Graph the solution and write the solution in interval notation.

    \(|x|\leq 8\)

    \(|2x−5|\leq 3\)

    Answer

    The solution is 1 is less than or equal to x which is less than or equal to 4. The number line shows a closed circle at 1, a closed circle at 4, and shading in between the circles. The interval notation is 1 to 4 within brackets.

    \(|6x−5|<7\)

    \(|5x+1|\leq −2\)

    Answer

    The solution is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.

    Solve Absolute Value Inequalities with “greater than”

    In the following exercises, solve. Graph the solution and write the solution in interval notation.

    \(|x|>6\)

    \(|x|\geq 2\)

    Answer

    The solution is x is less than negative 2 or x is greater than 6. The number line shows a closed circle at negative 2 with shading to its left and a closed circle at 2 with shading to its right. The interval notation is the union of negative infinity to negative 2 within a parenthesis and a bracket and 2 to infinity within a bracket and a parenthesis.

    \(|x−5|>−2\)

    \(|x−7|\geq 1\)

    Answer

    The solution is x is less than or equal to 6 or x is greater than or equal to 8. The number line shows a closed circle at 6 with shading to its left and a closed circle at 8 with shading to its right. The interval notation is the union of negative infinity to negative 6 within a parenthesis and a bracket and 8 to infinity within a bracket and a parenthesis.

    \(3|x|+4\geq 1\)

    Solve Applications with Absolute Value

    In the following exercises, solve. 

    A craft beer brewer needs 215,000 bottle per day. But this total can vary by as much as 5,000 bottles. What is the maximum and minimum expected usage at the bottling company?

    Answer

    The minimum to maximum expected usage is 210,000 to 220,000 bottles

    At Fancy Grocery, the ideal weight of a loaf of bread is 16 ounces. By law, the actual weight can vary from the ideal by 1.5 ounces. What range of weight will be acceptable to the inspector without causing the bakery being fined?

    Practice Test

    In the following exercises, solve each equation.

    \(−5(2x+1)=45\)

    Answer

    \(x=−5\)

    \(\frac{1}{4}(12m+28)=6+2(3m+1)\)

    \(8(3a+5)−7(4a−3)=20−3a\)

    Answer

    \(a=41\)

    \(0.1d+0.25(d+8)=4.1\)

    \(14n−3(4n+5)=−9+2(n−8) \)

    Answer

    contradiction; no solution

    \(3(3u+2)+4[6−8(u−1)]=3(u−2)\)

    \(\frac{3}{4}x−\frac{2}{3}=\frac{1}{2}x+\frac{5}{6}\)

    Answer

    \(x=6\)

    \(|3x−4|=8\)

    \(|2x−1|=|4x+3|\)

    Answer

    \(x=−2,x=−13\)

    Solve the formula
    \(x+2y=5\) for y.

    In the following exercises, graph the inequality on the number line and write in interval notation.

    \(x\geq −3.5\)

    Answer

    The inequality is x is greater than or equal to negative 3.5. The number line shows a left bracket at negative 3.5 and shading to the right. The interval notation is negative 3.5 to infinity within a bracket and a parenthesis.

    \(x<\frac{11}{4}\)

    \(−2\leq x<5\)

    Answer

    The inequality is negative two is less than or equal to x which is less than 5. The number line shows a closed circle at negative 2 and an open circle at 5 with shading between the circles. The interval notation is negative 2 to 5 within a bracket and a parenthesis.

    In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 

    \(8k\geq 5k−120\)

    \(3c−10(c−2)<5c+16\)

    Answer

    The solution is c is greater than one-third. The number line shows a left parenthesis at one-third with shading to its right. The interval notation is one-third to infinity within parentheses.

    \(\frac{3}{4}x−5\geq −2\) and
    \(−3(x+1)\geq 6\)

    \(3(2x−3)<−5\) or
    \(4x−1>3\)

    Answer

    The solution is x is less than two-thirds or x is greater than 1. The number line shows an open circle at two-thirds with shading to its left and an open circle at 1 with shading to its right. The interval notation is the union of negative infinity to two-thirds within parentheses and 1 to infinity within parentheses.

    \(\frac{1}{2}x−3\leq 4\) or
    \(\frac{1}{3}(x−6)\geq −2\)

    \(|4x−3|\geq 5\)

    Answer

    The solution is x is less than or equal to negative one-half or x is greater than or equal to 2. The number line shows a closed circle at negative one-half with shading to its left and a closed circle at 2 with shading to its right. The interval notation is the union of negative infinity to negative one-half within a parenthesis and bracket and 2 to infinity within a bracket and a parenthesis.

    In the following exercises, translate to an equation or inequality and solve.

    Four less than twice x is 16.

    Find the length of the missing side.

    The figure is a right triangle with a base of 6 units and a height of 9 units.

    Answer

    \(10.8\)

    One number is four more than twice another. Their sum is \(−47\). Find the numbers.

    The sum of two consecutive odd integers is \(−112\).. Find the numbers.

    Answer

    \(−57,−55\)

    Marcus bought a television on sale for $626.50 The original price of the television was $895. Find ⓐ the amount of discount and ⓑ the discount rate.

    Bonita has $2.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she have?

    Answer

    12 dimes, seven quarters

    Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs $5.71 per gallon?

    The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.

    Answer

    \(30°,60°,90°\)

    The length of a rectangle is five feet more than four times the width. The perimeter is 60 feet. Find the dimensions of the rectangle. 

    Two planes leave Dallas at the same time. One heads east at a speed of 428 miles per hour. The other plane heads west at a speed of 382 miles per hour. How many hours will it take them to be 2,025 miles apart?

    Answer

    \(2.5\) hours 

    Leon drove from his house in Cincinnati to his sister’s house in Cleveland, a distance of 252 miles. It took him \(4\frac{1}{2}\) hours. For the first half hour, he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?

    Sara has a budget of $1,000 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?

    Answer

    At most $55.56 per costume.