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# 4.13: Convert Customary Units of Measurement in Real-World Situations

Difficulty Level: At Grade Created by: CK-12
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Practice Applications of Customary Unit Conversions
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Evana is making a recipe for fruit punch that uses 3 cups of pineapple juice. If she makes 5 batches of the recipe, how many quarts of pineapple juice will she need?

In this concept, you will learn to convert customary units of measurement in real-world situations.

### Customary System

The customary system, also known as the Imperial System, is made up of units such as inches, feet, cups, gallons and pounds. Let’s look at conversions within the customary system of measurement.

Customary Units of Measurement

Let’s look at an example.

The distance from John’s house to Mike’s house on a map is 4.5 inches. The scale of the map is 1.5 inches=2 miles\begin{align*}1.5 \text{ inches}= 2 \text{ miles}\end{align*}. What is the actual distance from John’s house to Mike’s house in feet?

First, set up a proportion.

1.5 inches2 miles=4.5 inchesx miles\begin{align*}\frac{1.5 \text{ inches}}{2 \text{ miles}}=\frac{4.5 \text{ inches}}{x \text{ miles}}\end{align*}

Next, cross multiply.

1.521.5x1.5x===4.5x2×4.59\begin{align*}\begin{array}{rcl} \frac{1.5}{2} &=& \frac{4.5}{x} \\ 1.5x &=& 2 \times 4.5 \\ 1.5x &=& 9 \end{array} \end{align*}

Then, divide both sides by 1.5 to solve for x\begin{align*}x\end{align*}.

1.5x1.5x1.5x===991.56\begin{align*}\begin{array}{rcl} 1.5x &=& 9 \\ \frac{1.5x}{1.5}&=&\frac{9}{1.5} \\ x &=& 6 \end{array} \end{align*}

Then, if the actual distance is 6 miles, what is this distance in feet.

1 mile5280 feet=6 milesx feet\begin{align*}\frac{1 \text{ mile}}{5280 \text{ feet}}= \frac{6 \text{ miles}}{x \text{ feet}}\end{align*}

Then, cross multiply to solve for x\begin{align*}x\end{align*} .

152801xx===6x6×528031680\begin{align*}\begin{array}{rcl} \frac{1}{5280} &=& \frac{6}{x} \\ 1x &=& 6 \times 5280 \\ x &=& 31680 \end{array}\end{align*}

The distance between the two houses is 31,680 feet.

### Examples

#### Example 1

Earlier, you were given a problem about Evana and her thirsty conversion.

Evana needs to make 5 batches with each batch needing 3 cups of juice. She needs to find the total amount of juice in quarts.

First, find the total number of cups she needs. If there are 3 cups in one batch, and she is making 5 batches, then she will need:

3×5=15 cups\begin{align*}3 \times 5 = 15 \text{ cups}\end{align*}

Next, set up a proportion.

4 cups1 quart=15 cupsx quarts\begin{align*}\frac{4 \text{ cups}}{1 \text{ quart}} = \frac{15 \text{ cups}}{x \text{ quarts}}\end{align*}

Then, cross multiply.

414x4x===15x1×1515\begin{align*}\begin{array}{rcl} \frac{4}{1} &=& \frac{15}{x} \\ 4x &=& 1 \times 15 \\ 4x &=& 15 \end{array} \end{align*}

Then, divide both sides by 4 to solve for x\begin{align*}x\end{align*}.

4x4x4x===151543.75\begin{align*}\begin{array}{rcl} 4x &=& 15 \\ \frac{4x}{4} &=& \frac{15}{4} \\ x &=& 3.75 \end{array} \end{align*}

Evana needs to make 3.75 quarts of punch.

#### Example 2

A scale model of a building has a height of 3.5 feet. The scale of the model is  112 inch=10 feet\begin{align*}1 \frac{1}{2} \text{ inch}= 10 \text{ feet}\end{align*}. What is the actual height of the building?

First, set up a proportion to find the height in inches.

12 inches1 foot=x inches3.5 feet\begin{align*}\frac{12 \text{ inches}} {1 \text{ foot}} = \frac{x \text{ inches}}{3.5 \text{ feet}}\end{align*}

Next, cross multiply to solve for x\begin{align*}x\end{align*}.

1211xx===x3.512×3.542\begin{align*}\begin{array}{rcl} \frac{12}{1} &=& \frac{x}{3.5} \\ 1x &=& 12 \times 3.5 \\ x &=& 42 \end{array}\end{align*}

The scale model is 42 inches high.

Then, set up a proportion to solve for the actual height of the building.

1.5 inches10 feet=42 inchesx feet\begin{align*}\frac{1.5 \text{ inches}}{10 \text{ feet}} = \frac{42 \text{ inches}}{x \text{ feet}}\end{align*}

Then, cross multiply.

1.5101.5x1.5x===42x10×42420\begin{align*}\begin{array}{rcl} \frac{1.5}{10} &=& \frac{42}{x} \\ 1.5x &=& 10 \times 42 \\ 1.5x &=& 420 \end{array}\end{align*}

Then, divide both sides by 1.5 in order to solve for x\begin{align*}x\end{align*}.

1.5x1.5x1.5x===4204201.5280\begin{align*}\begin{array}{rcl} 1.5x &=& 420 \\ \frac{1.5x}{1.5} &=& \frac{420}{1.5} \\ x &=& 280 \end{array}\end{align*}

The building is 280 feet tall.

#### Example 3

Karin has a recipe that calls for 3 gallons of cider. How many quarts will she need?

First, set up a proportion.

1 gallon4 quarts=3 gallonsx quarts\begin{align*}\frac{1\text{ gallon}}{4 \text{ quarts}} = \frac{3 \text{ gallons}}{x \text{ quarts}}\end{align*}

Next, cross multiply to solve for x\begin{align*}x\end{align*}.

141xx===3x3×412\begin{align*}\begin{array}{rcl} \frac{1}{4} &=& \frac{3}{x} \\ 1x &=& 3 \times 4 \\ x &=& 12 \end{array} \end{align*}

Karin will need 12 quarts of cider.

#### Example 4

Jack threw the ball 12 feet. How many inches did he throw the ball?

First, set up a proportion.

1 foot12 inches=12 feetx inches\begin{align*}\frac{1 \text{ foot}}{12 \text{ inches}} = \frac{12 \text{ feet}}{x\text{ inches}}\end{align*}

Next, cross multiply to solve for x\begin{align*}x\end{align*}.

1121xx===12x12×12144\begin{align*}\begin{array}{rcl} \frac{1}{12} &=&\frac{12}{x} \\ 1x &=& 12 \times 12 \\ x &=& 144 \end{array} \end{align*}

Jack threw the ball 144 inches.

#### Example 5

Carl drank 3 pints of lemonade. How many ounces did he drink?

First, set up a proportion.

1 pint16 ounces=3 pintsx ounces\begin{align*}\frac{1 \text{ pint}}{16 \text{ ounces}} = \frac{3 \text{ pints}}{x \text{ ounces}}\end{align*}

Next, cross multiply to solve for x\begin{align*}x\end{align*}.

1161xx===3x16×348\begin{align*}\begin{array}{rcl} \frac{1}{16} &=& \frac{3}{x} \\ 1x &=& 16 \times 3 \\ x &=& 48 \end{array} \end{align*}

Carl drank 48 ounces of lemonade.

### Review

Solve each problem.

1. Justin ran 3 miles. How many feet did he run?
2. If the flour weighed four pounds, how many ounces did it weigh?
3. How many pounds is equal to 4 tons?
4. Mary needs 3 cups of juice for a recipe. How many ounces does she need?
5. Jess bought 3 quarts of pineapple juice. How many pints did she purchase?
6. If Karen bought 16 quarts of ice cream, how many gallons did she buy?
7. The length of the garden is four yards. How many feet is that?
8. If the width of the garden is 4 yards, how many inches is that?
9. Will eight cups of water fit in a two quart saucepan?
10. A recipe calls for 2 pints of milk. If Jorge cuts the recipe in half, how many cups of milk will he need?
11. Audrey is making brownies for a bake sale. The recipe calls for 8 ounces of flour for every 24 brownies. If she makes 96 brownies, how many pounds of flour will she need?
12. Two buildings are 5 inches apart on a map. The scale on the map is 14 inch=1 mile\begin{align*}\frac{1}{4} \text{ inch}=1 \text{ mile}\end{align*}. What is the actual distance between the two buildings?
13. The length of a classroom on a floor plan is 2.5 inches. The scale of the map is 12 inches=5 feet\begin{align*}\frac{1}{2} \text{ inches}= 5 \text{ feet}\end{align*} What is the actual length of the classroom in inches?
14. A scale model of a mountain is 2.75 feet tall. The scale of the model is 14 inch=50  feet\begin{align*}\frac{1}{4}\text{ inch}=50 \ \text{ feet}\end{align*} What is the actual height of the mountain in feet?
15. A scale drawing of a town includes a park that measures 0.5 inch by 1.5 inches. If the scale of the map is 0.5 inches=1 mile\begin{align*}0.5 \text{ inches} = 1\text{ mile}\end{align*}, what is the area of the park in square feet?

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Color Highlighted Text Notes

### Vocabulary Language: English

Customary System

The customary system is the measurement system commonly used in the United States, including: feet, inches, pounds, cups, gallons, etc.

Measurement

A measurement is the weight, height, length or size of something.

Proportion

A proportion is an equation that shows two equivalent ratios.

Ratio

A ratio is a comparison of two quantities that can be written in fraction form, with a colon or with the word “to”.

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