# 2.6E: Exercises


## Practice Makes Perfect

Solve Proportions

In the following exercises, solve.

##### Example $$\PageIndex{31}$$

$$\frac{x}{56}=\frac{7}{8}$$

$$49$$

##### Example $$\PageIndex{32}$$

$$\frac{n}{91}=\frac{8}{13}$$

##### Example $$\PageIndex{32}$$

$$\frac{49}{63}=\frac{z}{9}$$

$$7$$

##### Example $$\PageIndex{33}$$

$$\frac{56}{72}=\frac{y}{9}$$

##### Example $$\PageIndex{34}$$

$$\frac{5}{a}=\frac{65}{11}$$

$$9$$

##### Example $$\PageIndex{35}$$

$$\frac{4}{b}=\frac{64}{144}$$

##### Example $$\PageIndex{36}$$

$$\frac{98}{154}=−\frac{7}{p}$$

$$−11$$

##### Example $$\PageIndex{37}$$

$$\frac{72}{156}=−\frac{6}{q}$$

##### Example $$\PageIndex{38}$$

$$\frac{a}{−8}=\frac{−42}{48}$$

$$7$$

##### Example $$\PageIndex{39}$$

$$\frac{b}{−7}=\frac{−30}{42}$$

##### Example $$\PageIndex{40}$$

$$\frac{2.7}{j}=\frac{0.9}{0.2}$$

$$0.6$$

##### Example $$\PageIndex{41}$$

$$\frac{2.8}{k}=\frac{2.1}{1.5}$$

##### Example $$\PageIndex{42}$$

$$\frac{a}{a+12}=\frac{4}{7}$$

$$16$$

##### Example $$\PageIndex{43}$$

$$\frac{b}{b−16}=\frac{11}{9}$$

##### Example $$\PageIndex{44}$$

$$\frac{c}{c−104}=−\frac{5}{8}$$

$$−\frac{5}{8}$$

##### Example $$\PageIndex{45}$$

$$\frac{d}{d−48}=−\frac{13}{3}$$

##### Example $$\PageIndex{46}$$

$$\frac{m+90}{25}=\frac{m+30}{15}$$

$$60$$

##### Example $$\PageIndex{47}$$

$$\frac{n+10}{4}=\frac{40−n}{6}$$

##### Example $$\PageIndex{48}$$

$$\frac{2p+4}{8}=\frac{p+18}{6}$$

$$30$$

##### Example $$\PageIndex{49}$$

$$\frac{q−2}{2}=\frac{2q−7}{18}$$

##### Example $$\PageIndex{50}$$

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 45 pounds?

9 ml

##### Example $$\PageIndex{51}$$

Brianna, who weighs 6 kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at 15 milligrams (mg) for every 1 kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?

##### Example $$\PageIndex{52}$$

A veterinarian prescribed Sunny, a 65 pound dog, an antibacterial medicine in case an infection emerges after her teeth were cleaned. If the dosage is 5 mg for every pound, how much medicine was Sunny given?

325 mg

##### Example $$\PageIndex{53}$$

Belle, a 13 pound cat, is suffering from joint pain. How much medicine should the veterinarian prescribe if the dosage is 1.8 mg per pound?

##### Example $$\PageIndex{54}$$

A new energy drink advertises 106 calories for 8 ounces. How many calories are in 12 ounces of the drink?

159 calories

##### Example $$\PageIndex{55}$$

One 12 ounce can of soda has 150 calories. If Josiah drinks the big 32 ounce size from the local mini-mart, how many calories does he get?

##### Example $$\PageIndex{56}$$

A new 7 ounce lemon ice drink is advertised for having only 140 calories. How many ounces could Sally drink if she wanted to drink just 100 calories?

5 oz

##### Example $$\PageIndex{57}$$

Reese loves to drink healthy green smoothies. A 16 ounce serving of smoothie has 170 calories. Reese drinks 24 ounces of these smoothies in one day. How many calories of smoothie is he consuming in one day?

##### Example $$\PageIndex{64}$$

Ronald needs a morning breakfast drink that will give him at least 390 calories. Orange juice has 130 calories in one cup. How many cups does he need to drink to reach his calorie goal?

3 cups

##### Example $$\PageIndex{65}$$

Sarah drinks a 32-ounce energy drink containing 80 calories per 12 ounce. How many calories did she drink?

##### Example $$\PageIndex{66}$$

Elizabeth is returning to the United States from Canada. She changes the remaining 300 Canadian dollars she has to $230.05 in American dollars. What was$1 worth in Canadian dollars?

1. 19 gallons
##### Example $$\PageIndex{88}$$

Lawn Fertilizer Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,000 square feet of lawn. Phil’s lawn is approximately 13,500 square feet. How many bags of fertilizer will he have to buy?

4 bags

##### Example $$\PageIndex{89}$$

House Paint April wants to paint the exterior of her house. One gallon of paint covers about 350 square feet, and the exterior of the house measures approximately 2000 square feet. How many gallons of paint will she have to buy?​​​​​​​

##### Example $$\PageIndex{90}$$

Cooking Natalia’s pasta recipe calls for 2 pounds of pasta for 1 quart of sauce. How many pounds of pasta should Natalia cook if she has 2.5 quarts of sauce?

5

##### Example $$\PageIndex{91}$$

Heating Oil A 275 gallon oil tank costs \$400 to fill. How much would it cost to fill a 180 gallon oil tank?​​​​​​​

## Writing Exercises

##### Example $$\PageIndex{92}$$

Marisol solves the proportion $$\frac{144}{a}=\frac{9}{4}$$ by ‘cross multiplying’, so her first step looks like 4·144=9·a. Explain how this differs from the method of solution shown in Example.

##### Example $$\PageIndex{93}$$

Find a printed map and then write and solve an application problem similar to Example.​​​​​​​

## Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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