2.E: Back To The Basics (Exercises)

2.1: Order of Operations

Hint: If a question involves money, round the answers to the nearest cent.

Mechanics

1. \(81 \div 27+3 \times 4\)
2. \(100 \div(5 \times 4-5 \times 2)\)
3. \(3^{3}-9+(1+7 \times 3)\)
4. \((6+3)^{2}-17 \times 3+70\)
5. \(100-\left(4^{2}+3\right)-(3+9 \times 3-4)\)

Applications

6. \(\left[\left(7^{2}-\{-41\}\right)-5 \times 2\right] \div(80-10)\)
7. \(\$ 1,000\left(1+0.09 \times \dfrac{88}{365}\right)\)
8. \(3\left[\$ 2,000(1+0.003)^{8}\right]+\$ 1,500\)
9. \(\dfrac{\$ 20,000}{1+0.07 \times \frac{7}{12}}\)
10. \(4 \times\left[\left(5^{2}+15\right)^{2} \div\left(13^{2}-9\right)\right]^{2}\)
11. \(\$ 500\left[\dfrac{(1+0.00875)^{43}-1}{0.00875}\right]\)
12. \(\$ 1,000\left(1+\dfrac{0.12}{6}\right)^{15}\)

Challenge, Critical Thinking, & Other Applications

13. \(\left(\dfrac{\$ 2,500}{1+0.10}\right)+\left(\dfrac{\$ 7,500}{(1+0.10)^{2}}\right)+\left(\dfrac{-\$ 1,500}{(1+0.10)^{3}}\right)+\left(\dfrac{-\$ 2,000}{(1+0.10)^{4}}\right)\)
14. \(\$ 175,000(1+0.07)^{15}+\$ 14,000\left[\dfrac{(1+0.07)^{20}-1}{0.07}\right]\)
15. \(\$ 5,000\left[\dfrac{\left\{1+\left[(1+0.08)^{0.5}-1\right]\right\}^{75}-1}{(1+0.08)^{0.5}-1}\right]\)
16. \(\$ 800\left[\dfrac{(1+0.07)^{20}-(1+0.03)^{20}}{0.07-0.03}\right]\)
17. \(\$ 60,000(1+0.0058)^{80}-\$ 450\left[\dfrac{(1+0.0058)^{25}-1}{0.0058}\right]\)
18. \(\left(\dfrac{0.08}{2}\right) \$ 1,000\left[\dfrac{1-\frac{1}{\left\{1+\left(\dfrac{0.08}{2}\right)\right\}^{16}}}{\left(\dfrac{0.08}{2}\right)}\right]+\$ 1,000\left[1+\left(\dfrac{0.08}{2}\right)\right]^{16}\)
19. \(\$ 1,475\left[\dfrac{\left(1+\dfrac{0.06}{4}\right)^{16}-1}{\dfrac{0.06}{4}}\right]\)
20. \(\$ 6,250(1+0.0525)^{10}+\$ 325\left[\dfrac{(1+0.0525)^{10}-1}{0.0525}\right]\)

2.2: Fractions, Decimals, and Rounding

Mechanics

1. For each of the following, identify the type of fraction presented.
   1. \(\dfrac{1}{8}\)
   2. \(3 \dfrac{3}{4}\)
   3. \(\dfrac{10}{9}\)
   4. \(\dfrac{34}{49}\)
   5. \(1 \dfrac{\dfrac{2}{3}}{9 \dfrac{5}{3}}\)
   6. \(\dfrac{56}{27}\)
   7. \(\dfrac{10 \dfrac{1}{5}}{9}\)
   8. \(\dfrac{6}{11}\)
2. In each of the following equations, identify the value of the unknown term.
   1. \(\dfrac{3}{4}=\dfrac{x}{36}\)
   2. \(\dfrac{y}{8}=\dfrac{16}{64}\)
   3. \(\dfrac{2}{z}=\dfrac{18}{45}\)
   4. \(\dfrac{5}{6}=\dfrac{75}{p}\)
3. Take each of the following fractions and provide one example of the fraction expressed in both higher and lower terms.
   1. \(\dfrac{5}{10}\)
   2. \(\dfrac{6}{8}\)
4. Convert each of the following fractions into decimal format.
   1. \(\dfrac{7}{8}\)
   2. \(15 \dfrac{5}{4}\)
   3. \(\dfrac{13}{5}\)
   4. \(133 \dfrac{\dfrac {17}{2}}{3 \dfrac{2}{5}}\)
5. Convert each of the following fractions into decimal format and round to three decimals.
   1. \(\dfrac{7}{8}\)
   2. \(15 \dfrac{3}{4}\)
   3. \(\dfrac{10}{9}\)
   4. \(\dfrac{15}{32}\)
6. Convert each of the following fractions into decimal format and express in repeating decimal notation.
   1. \(\dfrac{1}{12}\)
   2. \(5 \dfrac{8}{33}\)
   3. \(\dfrac{4}{3}\)
   4. \(\dfrac{-34}{110}\)

Applications

7. Calculate the solution to each of the following expressions. Express your answer in decimal format.
   1. \(\dfrac{1}{5}+3 \dfrac{1}{4}+\dfrac{5}{2}\)
   2. \(\dfrac{1 \dfrac{3}{8}}{2}-\dfrac{11}{40}+19 \dfrac{1}{2} \times \dfrac{3}{4}\)
8. Calculate the solution to each of the following expressions. Express your answer in decimal format with two decimals.
   1. \(\left(1+\dfrac{0.11}{12}\right)^{4}\)
   2. \(1-0.05 \times \dfrac{263}{365}\)
   3. \(200\left[1-\dfrac{1}{\left(1+\dfrac{0.10}{4}\right)^{2}}\right]\)
9. Calculate the solution to each of the following expressions. Express your answer in repeating decimal notation as needed.
   1. \(\dfrac{1}{11}+3 \dfrac{1}{9}\)
   2. \(\dfrac{5}{3}-\dfrac{7}{6}\)

Questions 10–14 involve fractions. For each, evaluate the expression and round your answer to the nearest cent.

10. \(\$ 134,000(1+0.14 \times 23 / 365)\)
11. \(\$ 10,000\left(1+\dfrac{0.0525}{2}\right)^{13}\)
12. \(\dfrac{\$ 535,000}{\left(1+\dfrac{0.07}{12}\right)^{3}}\)
13. \(\$ 2,995\left(1+0.13 \times \dfrac{90}{365}\right)-\dfrac{\$ 400}{1+0.13 \times \dfrac{15}{365}}\)
14. \(\dfrac{\$ 155,600}{\left(1+\dfrac{0.06}{12}\right)^{8}}\)

Challenge, Critical Thinking, & Other Applications

Questions 15–20 involve more complex fractions and reflect business math equations encountered later in this textbook. For each, evaluate the expression and round your answer to the nearest cent.

15. \(\dfrac{\$ 648}{0.0575 / 12}\left[1-\dfrac{1}{\left(1+\dfrac{0.0575}{12}\right)^{7}}\right]\)
16. \(\dfrac{\$ 10,000}{\left(1+\dfrac{0.115}{4}\right)^{2}}+\$ 68 \dfrac{\left[1-\dfrac{1}{\left(1+\dfrac{0.115}{4}\right)^{2}}\right]}{\dfrac{0.115}{4}}\)
17. \(\dfrac{\$ 2,000,000}{\left[\dfrac{\left(1+\dfrac{0.665}{2}\right)^{12}-1}{\dfrac{0.065}{2}}\right]}\)
18. \(\$ 8,500\left[\dfrac{1-\left(\dfrac{1}{1.08}\right)^{4}}{1.08}\right]+\$ 19,750\left(\dfrac{1}{1.08}\right)^{4}-\$ 4,350\)
19. \(\$ 15,000\left[\dfrac{\left(1+\dfrac{0.058}{4}\right)^{16}-1}{\dfrac{0.058}{4}}\right]\)
20. \(\dfrac{0.08}{2}(\$ 1,000)\left[\dfrac{1-\dfrac{1}{\left(1+\dfrac{0.07}{2}\right)^{10}}}{\dfrac{0.07}{2}}\right]+\$ 1,000 \dfrac{1}{\left(1+\dfrac{0.07}{2}\right)^{10}}\)

2.3: Percentages

Mechanics

1. Convert the following decimals into percentages.
   1. 0.4638
   2. 3.1579
   3. 0.000138
   4. 0.015
2. Convert the following fractions into percentages.
   1. \(\dfrac{3}{8}\)
   2. \(\dfrac{17}{32}\)
   3. \(\dfrac{42}{12}\)
   4. \(2 \dfrac{4}{5}\)
3. Convert the following fractions into percentages. Round to four decimals or express in repeating decimal format as needed.
   1. \(\dfrac{46}{12}\)
   2. \(\dfrac{2}{9}\)
   3. \(\dfrac{3}{11}\)
   4. \(\dfrac{48}{93}\)
4. Convert the following percentages into decimal form.
   1. 15.3%
   2. 0.03%
   3. 153.987%
   4. 14.0005%
5. What percentage of $40,000 is $27,000?
6. What is \(\dfrac{1}{2}\)% of $500,000?
7. $0.15 is 4,900% of what number?

Applications

8. In February 2009, 14,676 mortgages were in arrears in Canada, which represented 0.38% of all mortgages. How many total mortgages were in the Canadian market at that time?
9. In 2009, medical experts predicted that one out of two Manitobans would contract some form of the H1N1 virus. If the population of Manitoba in 2009 was 1,217,200, how many Manitobans were predicted to become ill?
10. In August 2004, Google Inc. offered its stocks to the public at $85 per share. In October 2007, the share price had climbed to $700.04. Express the 2007 share price as a percentage of the 2004 price.
11. During Michael Jordan's NBA career (1984–2003), he averaged a free throw completion percentage of 83.5% in regular season play. If Jordan threw 8,772 free throws in his career, how many completed free throws did he make?
12. If total advertising expenditures on television advertising declined 4.1% to $141.7 billion in the current year, how much was spent on television advertising in the previous year? Round your answer to one decimal.
13. If the new minimum wage of $8.75 per hour is 102.9412% of the old minimum wage, what was the old minimum wage?
14. A machine can produce 2,500 products per hour. If 37 of those products were defective, what is the defect rate per hour for the machine?

Challenge, Critical Thinking, & Other Applications

15. In 2011, Manitoba progressive income tax rates were 10.8% on the first $31,000, 12.75% on the next $36,000, and 17.4% on any additional income. If your gross taxable earnings for the year were $85,000, what percentage of your earnings did you pay in taxes?
16. In 2011, the maximum amount that you could have contributed to your RRSP (Registered Retirement Savings Plan) was the lesser of $22,450 or 18% of your earned income from the previous year. How much income do you need to claim a $22,450 contribution in 2011?
17. Maria, a sales representative for a large consumer goods company, is paid 3% of the total profits earned by her company. Her company averages 10% profit on sales. If Maria's total income for the year was $60,000, what total sales did her company realize?
18. A house was purchased six years ago for $214,000. Today it lists at a price that is 159.8131% of the original purchase price. In dollars, how much has the price of the house increased over the six years?
19. An investor buys 1,000 shares of WestJet Airlines at $10.30 per share. A few months later, the investor sells the shares when their value hits 120% of the original share price. What is the price of a WestJet share when the investor sells these shares? How much money did the investor make?
20. A Honda Insight has fuel economy of 3.2 litres consumed per 100 kilometres driven. It has a fuel tank capacity of 40 litres. A Toyota Prius is rated at 4.2 L per 100 km driven. It has a fuel tank capacity of 45 L. What percentage is the total distance driveable (rounded to the nearest kilometre before calculating) of a Honda Insight compared to that of a Toyota Prius?

2.4: Algebraic Expressions

Mechanics

For questions 1–4, simplify the algebraic expressions.

1. \(2 a-3 a+4+6 a-3\)
2. \(5b(4b + 2)\)
3. \(\dfrac{6 x^{3}+12 x^{2}+13.5 x}{3 x}\)
4. \((1+i)^{3} \times(1+i)^{14}\)
5. Evaluate the power \(8^{2 / 3}\)
6. Substitute the known variables and solve for the unknown variable:

\(I = Prt\) where \(P = \$2,500\), \(r = 0.06\), and \(t=\dfrac{135}{365}\)

Applications

For questions 7–11, simplify the algebraic expressions.

7. \(\left(6 r^{2}+10-6 r+4 r^{2}-3\right)-\left(-12 r-5 r^{2}+2+3 r\right)\)
8. \(\left[\dfrac{5 x^{9}+3 x^{9}}{2 x}\right]^{5}\)
9. \(\dfrac{t}{2}+0.75 t-t^{3}+\dfrac{5 t^{4}}{t}-\dfrac{2\left(t+t^{3}\right)}{4}\)
10. \(\dfrac{14(1+i)+21(1+i)^{4}-35(1+i)^{7}}{7(1+i)}\)
11. \(\dfrac{R}{1+0.08 \times \dfrac{183}{365}}+3 R\left(1+0.08 \times \dfrac{52}{365}\right)\)
12. Evaluate the power: \(\left[\left(\dfrac{2}{5}\right)^{2}\right]^{2}\)

For questions 13 and 14, substitute the known variables and solve for the unknown variable.

13. \(PV=\dfrac{FV}{(1+i)^{N}}\) where \(FV = \$3,417.24\), \(i = 0.05\), and \(N = 6\)
14. \(PMT=\dfrac{FV}{\left[\dfrac{(1+i)^{N}-1}{i}\right]}\) where \(FV = \$10,000\), \(N = 17\), and \(i = 0.10\)

Challenge, Critical Thinking, & Other Applications

For questions 15–17, simplify the algebraic expressions.

15. \(\left[\dfrac{10 a^{2} b^{3} c^{4}}{5 b^{3} c^{4}}\right]^{2}+6\left(a^{8}\right)^{1 / 2}-\left(3 a^{2}+6\right)\left(3 a^{2}-3\right)\)
16. \(\dfrac{-(5 x+4 y+3)(2 x-5 y)-(10 x-2 y)(2 y+3)}{5}\)
17. \(\dfrac{(-3 z)^{3}\left(3 z^{2}\right)^{2}}{\left(2 z^{3}\right)^{-4}}\)
18. Substitute the known variables and solve for the unknown variable.

\(FV_{ORD}=PMT(1+\Delta \%)^{N-1} \left[\dfrac{\left[\dfrac{(1+i)^{\dfrac{CY}{PY}}}{(1+\Delta \%)}\right]^{N}-1}{\dfrac{(1+i)^{\dfrac{CY}{PY}}}{(1+\Delta \%)}-1}\right]\) where \(PMT = \$500\), \(i = 0.05\), \(\Delta \% = 0.02\), \(CY = 2\), \(PY = 4\), and \(N = 20\)

For questions 19-20, evaluate the expression.

19. \(\$ 50,000 \times\left(1+\dfrac{0.10}{12}\right)^{-27}\)
20. \(\$ 995\left[\dfrac{1-(1+0.02)^{13}\left(1+\dfrac{0.09}{4}\right)^{-13}}{\dfrac{0.09}{4}-0.02}\right]\)

2.5: Linear Equations - Manipulating and Solving

Mechanics

Solve the following equations for the unknown variable.

1. \(3(x − 5) = 15\)
2. \(12b − 3 = 4 + 5b\)
3. \(0.75(4m + 12) + 15 − 3(2m + 6) = 5(−3m + 1) + 25\)

Solve each of the following pairs of equations for both unknown variables.

4. \(\begin{aligned} &x+y=6\\ &3 x-2 y=8 \end{aligned}\)
5. \(\begin{aligned} &4 h-7 q=13\\ &6 h+3 q=33 \end{aligned}\)
6. \(\begin{aligned} &0.25 a+\dfrac{5 b}{2}=3.5\\ &\dfrac{3 a}{4}-\dfrac{b}{0.2}=3 \end{aligned} \)

Applications

In questions 7 and 8, solve the equation for the unknown variable.

7. \(\dfrac{4 y}{1.025^{4}}+y-2 y(1.05)^{2}=\$ 1,500\)
8. \(\$ 2,500(1+0.06 t)+\$ 1,000(1+0.04 t)=\$ 3,553.62\)

For exercises 9–14, read each question carefully and solve for the unknown variable(s).

9. Pamela is cooking a roast for a 5:30 p.m. dinner tonight. She needs to set a delay timer on her oven. The roast takes 1 hour and 40 minutes to cook. The time right now is 2:20 p.m. How long of a delay must she set the oven for (before it automatically turns on and starts to cook the roast)?
10. In 2010, 266 million North Americans were using the Internet, which represented a 146.3% increase in Internet users over the year 2000. How many North American Internet users were there in 2000?
11. A human resource manager is trying to estimate the cost of a workforce accident. These costs usually consist of direct costs (such as medical bills, equipment damage, and legal expenses) and indirect costs (such as decreased output, production delays, and fines). From past experience, she knows that indirect costs average six times as much as direct costs. If she estimates the cost of an accident to be $21,000, what is the direct cost of the accident?
12. In 2011, Canadian federal tax rates were 0% on the first $10,527 of gross income earned, 15% on the next $31,017, 22% on the next $41,544, 26% on the next $45,712, and 29% on anything more. If a taxpayer paid $28,925.35 in federal tax, what was her gross annual income for 2011?
13. St. Boniface Hospital raises funds for research through its Mega Lottery program. In this program, 16,000 tickets are available for purchase at a price of one for $100 or three for $250. This year, the lottery sold out with sales of $1,506,050. To better plan next year's lottery, the marketing manager wants to know how many tickets were purchased under each option this year.
14. An accountant is trying to allocate production costs from two different products to their appropriate ledgers. Unfortunately, the production log sheet for last week has gone missing. However, from other documents he was able to figure out that 1,250 units in total were produced last week. The production machinery was run for 2,562.5 minutes, and he knows that Product A takes 1.5 minutes to manufacture while Product B takes 2.75 minutes to manufacture. How many units of each product were produced last week?

Challenge, Critical Thinking, & Other Applications

15. Jacob owns 15,000 shares in a corporation, which represents 2% of all issued shares for the company. He sold \(\frac{2}{5}\) of his shares to another investor for $7,800. What is the total value for all of the shares issued by the company?
16. Two cell phone companies are offering different rate plans. Rogers is offering $19.99 per month, which includes a maximum of 200 weekday minutes plus $0.35 for every minute above the maximum. TELUS is offering $39.99 for a maximum 300 weekday minutes, but it charges $0.10 for every minute above the maximum. Above how many minutes would TELUS be the better choice?
17. Marianne, William, Hendrick, and Charlotte have all decided to go into business together. They need $175,000 in initial capital funding. William was able to contribute 20% less than Marianne, Hendrick contributed 62.5% more than William, and Charlotte contributed $5,000 less than half as much as Marianne. How much did each partner contribute to the initial funds?
18. A mall is being constructed and needs to meet the legal requirements for parking availability. Parking laws require one parking stall for every 100 square feet of retail space. The mall is designed to have 1,200,000 square feet of retail space. Of the total parking stalls available, 2% need to be handicap accessible, there need to be three times as many small car spaces as handicap spaces, RV spaces need to be one-quarter of the number of small car spaces, and the rest of the spaces are for regular stalls. How many of each type of parking space does the mall require?
19. Simplify the following equation into the format of \(\#z = \#\) and find the root. Verify the solution through substitution.\[z\left(1+0.073 \times \dfrac{280}{365}\right)-\dfrac{z}{1+0.073 \times \dfrac{74}{365}}+\$ 1,000=\$ 2,764.60\nonumber \]
20. Find the roots for the following pairs of equations. Verify the solution through substitution into both equations.\[\begin{aligned} 3 \dfrac{4}{5} q+0.18 r&=12.2398 \\ -5.13 q-\dfrac{13 r}{5}&=-38.4674 \end{aligned} \nonumber \]

2.6: Natural Logarithms

Mechanics

Using your financial calculator, evaluate each of the following. Write your answer using the \(e^x =\) power format. Round your answers to six decimals.

1. \(\ln(3.9243)\)
2. \(\ln(0.7445)\)
3. \(\ln(1.83921)\)
4. \(\ln(13.2746)\)
5. \(\ln(0.128555)\)

Applications

For each of the following, demonstrate the fifth property of natural logarithms, where \(\ln \left(\dfrac{x}{y}\right)=\ln (x)-\ln (y)\).

6. \(\ln \left(\dfrac{\$ 28,500}{\$ 19,250}\right)\)
7. \(\ln \left(\dfrac{\$ 100,000}{\$ 10,000}\right)\)
8. \(\ln \left(\dfrac{\$ 75,000}{\$ 12,255}\right)\)

For each of the following, demonstrate the sixth property of natural logarithms, where \(\ln \left(x^{y}\right)=y(\ln x)\).

9. \(\ln \left[(1.02)^{23}\right]\)
10. \(\ln \left[(1.01275)^{41}\right]\)
11. \(\ln \left[(1.046)^{34}\right]\)

Using \(\dfrac{\ln \left(\dfrac{FV}{PV}\right)}{\ln (1+i)}\), substitute the known values and evaluate the expression.

	\(FV\)	\(PV\)	\(i\)
12.	$78,230	$25,422	0.0225
13.	$233,120	$91,450	0.0425
14.	$18,974	$8,495	0.02175

Challenge, Critical Thinking, & Other Applications

Using \(FV=PV(1+i)^{N}\), substitute in the known values and solve for \(N\).

	\(FV\)	\(PV\)	\(i\)
15.	$18,302.77	$14,000.00	0.015
16.	$58,870.20	$36,880	0.01

Review Exercises

Mechanics

1. Solve the following expression: \(\left(1+\dfrac{0.0725}{12}\right)^{\tfrac{2}{4}}-1\)
2. Convert the following into a decimal format and express it in an appropriate manner: \(4 \dfrac{12}{37}\)
3. In Canadian five-pin bowling, the maximum score per game is 450. Alexandria just finished bowling a game of 321. What percentage of a perfect score does this represent?
4. Simplify the following algebraic expression: \(\dfrac{16 x^{2}}{4 x}-\dfrac{21 x^{3} y^{2}}{7 x^{2} y^{2}}\)
5. Solve the following equation for \(r\): \(-2 r-2.25=3.75-8 r\)
6. Demonstrate that \(3 \times \ln (2)=\ln \left(2^{3}\right)\).

Applications

7. Solve the following expression: \((0.06)(\$ 1,725)\left[\dfrac{1-\left(1+\dfrac{0.14}{4}\right)^{-7}}{\dfrac{0.14}{4}}\right] \)
8. Evaluate the following: \(\left[\dfrac{1+\dfrac{\dfrac{0.0975}{4} \times \$ 3,225}{\$255}}{1+\dfrac{0.0975}{4}}\right]\)
9. A 240 mL bottle of an orange drink claims that it is made with real fruit juice. Upon examination of the ingredient list, only 15% of the contents is actually fruit juice. How many millilitres of "other ingredients" are in the bottle?
10. On average across all industries, full-time employed Canadians worked 39.5 hours per week. If the typical adult requires eight hours of sleep per day, what percentage of the hours in a single week are left over for personal activities?
11. Substitute the given values in the following equation and solve: \(a\left[\dfrac{(1+b)^{c}-1}{b}\right]\) where \(a = \$535\), \(b = 0.025\), and \(c = 6\)
12. Simplify the following algebraic expression: \(\left(\dfrac{15 a^{7} b^{3} c^{2}}{5 a^{5} c}\right)^{3} \div\left(\dfrac{9 a^{4} b^{6} c^{5}}{3 a^{2} b^{2} c^{3}}\right)^{\frac{3}{2}}\)
13. Simplify the following algebraic expression: \(PMT\left[\dfrac{1-(1+0.0225)^{6}(1+0.044)^{-6}}{0.044-0.0225}\right]+PMT\left(\dfrac{1}{0.044}+1\right)\)
14. Housing starts in Winnipeg for the first half of the 2009 year were down 46.733% from 2008, when 1,500 new homes were started. How many housing starts were there in 2009?
15. A local baseball team sells tickets with two price zones. Seats behind the plate from first base to third base are priced at $20 per ticket. All other seats down the base lines and in the outfield are priced at $10 per ticket. At last night's game, 5,332 fans were in attendance and total ticket revenue was $71,750. How many tickets in each zone were sold?

Challenge, Critical Thinking, & Other Applications

16. An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is 93% of the industry average, Firm B's average salary is $58,000, and the industry average salary is 96% of Firm B's average salary.
    1. Determine the industry average salary.
    2. Determine Firm A's average salary.
    3. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.
17. Solve the following expression: \(\$ 500\left[\frac{\left(1+\left\{\left(1+\dfrac{0.07}{2}\right)^{4 / 12}-1\right\}\right)^{4}-1}{\left(1+\dfrac{0.07}{2}\right)^{4 / 12}-1}\right]\)
18. Francesca operates an online flower delivery business. She learned that in 2012 there were an estimated 324,000 online orders in her region, which represented a 1 12 increase over the previous year. Her business received 22,350 online orders in 2012, which represented a 3 14 increase over her previous year. In 2011, what percentage of online orders were placed with Francesca's business?
19. Goodyear Tires just completed a "Buy Three Get One Free" promotion on its ultra-grip SUV tires, regularly priced at $249.99 per tire. Over the course of the promotion, 1,405 tires were sold resulting in sales of $276,238.95. How many tires were sold at the regular price and how many tires were sold at the special promotional price?
20. The current price of $41.99 for a monthly cellphone rate plan is 105% of last year's rate plan. There are currently 34,543 subscribers to the plan, which is 98% of last year. Express the current total revenue as a percentage of last year's total revenue. Round the final answer to one decimal.

Contributors and Attributions

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