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Algebra 1

1.15.3 Using Direct Variation to Solve Application Problems, Part 1

Algebra 11.15.3 Using Direct Variation to Solve Application Problems, Part 1
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Activity

Return to your original group and work through this next part of your assigned problem. Then be ready to share.

When Raoul runs on the treadmill at the gym, the number of calories, c c , he burns varies directly with the number of minutes, m m , he uses the treadmill. He burned 315 calories when he used the treadmill for 18 minutes. 

How many calories would he burn if he ran on the treadmill for 25 minutes?

The number of calories, c c , burned varies directly with the amount of time, t t , spent exercising. Arnold burned 312 calories in 65 minutes exercising. 

How many calories would he burn if he exercises for 90 minutes?

The distance a moving body travels, d d , varies directly with time, t t , it moves. A train travels 100 miles in 2 hours.

How many miles would it travel in 5 hours?

Are you ready for more?

Extending Your Thinking

For example 1, how could you find out how many minutes Raoul would need to use the treadmill to burn a certain number of calories?

Video: Using Direct Variation to Solve Application Problems

Watch the following video to learn more about how to use direct variation to solve an application problem.

Access multimedia content

Self Check

Sophia is making parts for a model ship. The number of parts, p , she can make in a day varies directly with the number of hours, h , she works. She can make 28 parts in 4 hours. How many parts would Sophia make in 9 hours?
  1. 252
  2. 79
  3. 16
  4. 63

Additional Resources

Solve Application Problems Using Direct Variation

In applications using direct variation, generally we will know values of one pair of the variables and will be asked to find the equation that relates x x and y y . Then we can use that equation to find values of y y for other values of x x .

Here’s how to solve applications of direct variation problems.

Step 1 - Write the equation for direct variation. Identify the variables.

Step 2 - Substitute the given values for the variables.

Step 3 - Solve for the constant of variation.

Step 4 - Write the equation that relates x x and y y using the constant of variation.

Step 5 - Substitute the value for the variable.

Step 6 - Solve.

Let’s look at an application problem:

If the cost of a pizza varies directly with its diameter, and an 8-inch pizza costs $12, how much would a 6-inch pizza cost?

Step 1 - Write the equation for direct variation. Identify the variables.

y = k x y = k x

y y : cost of pizza, x x : diameter

Step 2 - Substitute the given values for the variables.

12 = k ( 8 ) 12 = k ( 8 )

Step 3 - Solve for the constant of variation.

k = 3 2 k = 3 2

Step 4 - Write the equation that relates x and y using the constant of variation.

y = 3 2 x y = 3 2 x

Step 5 - Substitute the value for the variable.

y = 3 2 ( 6 ) y = 3 2 ( 6 )

Step 6 - Solve.

y = 9 y = 9

What does this mean in the context of the problem?

A pizza that has a diameter of 6 inches costs $9.

Try it

Try It: Solve Application Problems Using Direct Variation

The number of buckets of water, b b , filled by a spring varies directly with the number of minutes, m m , passed. The spring fills 3 buckets of water in 14 minutes.

How many buckets would be filled in 42 minutes?

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