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

First, set up a proportion.

Next, cross multiply.

Then, divide both sides by 1.5 to solve for .

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

Then, cross multiply to solve for

.

The answer is 31680.

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:

Next, set up a proportion.

Then, cross multiply.

Then, divide both sides by 4 to solve for .

The answer is 3.75.

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 . What is the actual height of the building?

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

Next, cross multiply to solve for .

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.

Then, cross multiply.

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

.

The answer is 280.

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.

Next, cross multiply to solve for

.

The answer is 12.

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.

Next, cross multiply to solve for

.

The answer is 144.

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.

Next, cross multiply to solve for

.

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 . 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 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 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 , 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.