# 3.3.3: Conversion of Customary Length, Weight, and Capacity Applications

- Page ID
- 8745

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Convert Customary Units of Measurement in Real-World Situations

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. What is the actual distance from John’s house to Mike’s house in feet?

First, set up a **proportion**.

(1.5 inches)/(2 miles)=(4.5 inches)/(x miles)

Next, cross multiply.

1.5/2=4.5/x

1.5x=2×4.5

1.5x=9

Then, divide both sides by 1.5 to solve for x.

1.5x=9

1.5x/1.5=9/1.5

x=6

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

1 mile/5280 feet=6 miles/x feet

Then, cross multiply to solve for x .

1/5280=6/x

1x=6×5280

x=31,680

The answer is 31,680.

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

**Examples**

Example 3.3.3.1

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.

**Solution**

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

Next, set up a proportion.

4 cups/1 quart=15 cups/x quarts

Then, cross multiply.

4/1=15/x

4x=1×15

4x=15

Then, divide both sides by 4 to solve for x.

4x=15

4x/4=15/4

x=3.75

The answer is 3.75.

Evana needs to make 3.75 quarts of punch.

Example 3.3.3.2

A scale model of a building has a height of 3.5 feet. The scale of the model is 112 inch=10 feet. What is the actual height of the building?

**Solution**

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

12 inches/1 foot=x inches/3.5 feet

Next, cross multiply to solve for x.

12/1=x/3.5

1x=12×3.5

x=42

The answer is 42.

The scale model is 42 inches high.

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

1.5 inches/10 feet=42 inches/x feet

Then, cross multiply.

1.5/10=42/x

1.5x=10×42

1.5x=420

Then, divide both sides by 1.5 in order to solve for x.

1.5x=420

1.5x/1.5=420/1.5

x=280

The answer is 280.

The building is 280 feet tall.

Example 3.3.3.3

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

**Solution**

First, set up a proportion.

1 gallon/4 quarts=3 gallons/x quarts

Next, cross multiply to solve for x.

1/4=3/x

1x=3×4

x=12

The answer is 12.

Karin will need 12 quarts of cider.

Example 3.3.3.4

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

**Solution**

First, set up a proportion.

1 foot/12 inches=12 feet/x inches

Next, cross multiply to solve for x.

1/12=12/x

1x=12×12

x=144

The answer is 144.

Jack threw the ball 144 inches.

Example 3.3.3.5

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

**Solution**

First, set up a proportion.

1 pint/16 ounces=3 pints/x ounces

Next, cross multiply to solve for x.

1/16=3/x

1x=16×3

x=48

The answer is 48.

Carl drank 48 ounces of lemonade.

### Review

Solve each problem.

- Justin ran 3 miles. How many feet did he run?
- If the flour weighed four pounds, how many ounces did it weigh?
- How many pounds is equal to 4 tons?
- Mary needs 3 cups of juice for a recipe. How many ounces does she need?
- Jess bought 3 quarts of pineapple juice. How many pints did she purchase?
- If Karen bought 16 quarts of ice cream, how many gallons did she buy?
- The length of the garden is four yards. How many feet is that?
- If the width of the garden is 4 yards, how many inches is that?
- Will eight cups of water fit in a two quart saucepan?
- A recipe calls for 2 pints of milk. If Jorge cuts the recipe in half, how many cups of milk will he need?
- 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?
- Two buildings are 5 inches apart on a map. The scale on the map is 14 inch=1 mile. What is the actual distance between the two buildings?
- The length of a classroom on a floor plan is 2.5 inches. The scale of the map is 12 inches=5 feet What is the actual length of the classroom in inches?
- A scale model of a mountain is 2.75 feet tall. The scale of the model is 14 inch=50 feet What is the actual height of the mountain in feet?
- 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, what is the area of the park in square feet?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.13.

### Vocabulary

Term | Definition |
---|---|

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”. |

#### Additional Resources

PLIX Interactive: **The Price of a Unit**

Video:

Practice: **Conversion of Customary Length, Weight, and Capacity Applications**