WRITING AND SOLVING PROPORTIONS

Sports  A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 60 minutes? In Example 1, you will use a proportion to answer this question.

A proportion is an equation that states that two ratios are equivalent.

Algebra  = , where b and d are nonzero numbers.

EXAMPLE 1 USING EQUIVALENT RATIOS

Sports  A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 60 minutes? In Example 1, you will use a proportion to answer this question.

To find the number C of calories the person would burn while skateboarding for 60 minutes, solve the proportion = .

Answer: Ask yourself, what number can you multiply by 30 to get 60? The answer is 2. So, multiply 150 x 2 to get 300. So the person would burn about 300 calories while skateboarding for 60 minutes.

EXAMPLE 2 SOLVING PROPORTIONS USING ALGEBRA

Solve the proportion = .

EXAMPLE 2 WRITING AND SOLVING A PROPORTION

Setting Up a Proportion  There are different ways to set up a proportion. Consider the following problem.

Yesterday you bought 8 bagels for $4. Today you want only 5 bagels. How much will 5 bagels cost?

WRITING AND SOLVING A PROPORTION Empire State Building  At maximum

speed, the elevators in the Empire State Building can pass 80 floors in 45 seconds. Follow the steps below to find the number of floors that the elevators can pass in 9 seconds.

Step 1: Write a proportion:

Step 2: Solve the proportion: multiply both sides by 9

divide 720 by 45

16 = x

LESSON 5: SOLVING PROPORTIONS USING CROSS PRODUCTS

In the Real World Science  At space camp, you can sit in a

chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? You’ll find the answer in Example 2.

In the proportion , the products 2 • 6 and 3 • 4 are called cross products. Notice that the cross products are equal. This suggests the following property.

CROSS PRODUCTS PROPERTY

Cross Products Property

Words The cross products of a proportion are equal.

EXAMPLE 1 SOLVING A PROPORTION USING CROSS PRODUCTS

Use the cross products property to solve.

Science  At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon?

EXAMPLE 2 WRITING AND SOLVING A PROPORTION

Penguins  At an aquarium, the ratio of rockhopper penguins to African penguins is 3 to 7. If there are 50 penguins, how many are rockhoppers?

First, determine the ratio of rockhoppers to total penguins. Then, set up proportion.

EXAMPLE 3 WRITING AND SOLVING A PROPORTION

YOUR TURN

In John’s class, the ratio of boys to girls is 5 to 8. If there are 39 students in his class, how many are girls?