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# Applications of Customary Unit Conversions

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# Convert Customary Units of Measurement in Real-World Situations

Have you ever tried to measure accurately using different liquid units of measurement? Take a look at this dilemma.

Evan is making a recipe for fruit punch that uses 3 cups of pineapple juice. If he makes 5 batches of the recipe, how many quarts of pineapple juice will he need?

Pay attention to this Concept and you will learn how to apply customary units of measurement in real-world situations.

### Guidance

When we measure in the United States, we often use the customary system of measurement. The customary system is made up of units such as inches, feet, cups, gallons and pounds.

Now let's look at conversions within the customary system of measurement.

Customary Units of Measurement

Take a few minutes to copy all of these units of measurement down in your notebook.

Now let’s look at how we convert among customary units of measurement.

While you may be able to complete some of the mathematics in your head, it may make more sense to use a proportion. Because there is a relationship between different units of measure, you can use proportions to help you convert between customary units of measurement.

Then you can apply these conversions to real-world problems.

Take a look at this situation.

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, find the actual distance in miles. Then convert miles to feet.

Write a proportion to find the actual distance between the two houses.

$\frac{1.5 \ inches}{2 \ miles} = \frac{4.5 \ inches}{x \ miles}$

Now cross-multiply and solve for $x$ .

$(1.5)x &= 4.5(2)\\1.5x &= 9\\x &= 6$

So the two houses are 6 miles apart. Now convert miles to feet.

$\frac{1 \ mile}{5280 \ feet} = \frac{6 \ miles}{x \ feet}$

Now cross multiply to solve for $x$ .

$(1)x &= 6(5280)\\x &= 31,680$

The two houses are 31.680 feet apart.

Here is another one.

Jeff ran his weekly long run of 13 miles in 2 hours. If his rate is 9.23 per mile, how long would it take Jeff to run 5280 feet?

To figure this out, you can use a proportion, but it might make more sense to think in terms of customary units of measurement. Here Jeff runs 9.23 per mile.

How many feet are in one mile?

Yes, there are 5280 feet in one mile.

Therefore, Jeff runs 1 mile in 9.23.

Convert each customary unit of measurement.

#### Example A

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

Solution:  $12$ quarts

#### Example B

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

Solution: $144$ inches

#### Example C

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

Solution:  $48$ ounces

Now let's go back to the dilemma from the beginning of the Concept.

First find the total number of cups he needs.

If there are 3 cups in one batch, and he is making 5 batches, then he will need $3 \times 5 = 15 \ cups$ .

Set up a proportion.

The conversion factor is the number of cups in a quart: $\frac{4 \ cups}{1 \ quart}$ .

Now write the second ratio, making sure it follows the form of the first ratio.

$\frac{4 \ cups}{1 \ quart} = \frac{15 \ cups}{x \ quarts}$

Next cross-multiply and solve for $x$ .

$(4)x &= 1(15)\\4x &= 15\\x &= \frac{15}{4} = 3 \frac{3}{4}$

He will need $3 \frac{3}{4}$ quarts of pineapple juice.

### Vocabulary

Customary System
the system of measurement that includes inches, feet, miles, pounds, tons, cups, quarts, gallons, etc.

### Guided Practice

Here is one for you to try on your own.

A scale model of a building has a height of 3.5 feet. The scale of the model is $1 \frac{1}{2} \ inch = 10 \ feet$ . What is the actual height of the building?

Solution

The scale is in inches, but the scale model height is given in feet. First convert the scale height to inches. Then find the height of the building.

$\frac{1 \ foot}{12 \ inches} = \frac{3.5 \ feet}{x \ inches}$

Now cross multiply to solve for $x$ .

$(1)x &= 3.5(12)\\x &= 42$

So the height of the scale model is 42 inches. Now find the height of the actual building.

$\frac{1.5 \ inch}{10 \ feet} = \frac{42 \ inches}{x \ feet}$

Now cross multiply and solve for $x$ .

$(1.5)x &= 42(10)\\1.5x &= 420\\x &= 280$

The actual building is 280 feet tall.

### Practice

Directions: 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 of the map is $\frac{1}{4} \ inch = 1 \ mile$ . 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 $\frac{1}{2} \ inch = 5 \ feet$ . 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 $\frac{1}{4} \ inch = 50 \ feet$ . 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 $\frac{1}{2} \ inch = 1 \ mile$ , what is the area of the park in square feet?