In this activity, you will create a linear equation to model a real-world situation. Then you will solve the equation to find the solution. Gavin likes biking. He never misses a chance to go for a ride when the weather is nice. This week his goal is to bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before. How far should he ride on each of the four days to reach his goal?

Question 1
To solve this problem, first you need to write the expressions for the distance Gavin needs to bike each day. Then, relate these expressions to create an equation that represents Gavin’s situation.

Part A

If x is the number of miles Gavin bikes on the first day, write an expression for the distance he should bike on each of the following three days.

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Part B
Write an expression representing the total distance he should bike over the four days in terms of how far he bikes on the first day, x. Do not combine like terms.

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Part C
Because his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, x? Do not combine like terms.

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Part D
Which terms in the equation you found in part C are like terms involving x?

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Question 2
Now that you have the equation, solve it to find the number of miles Gavin should ride on each of the four days.

Part A

Combine the like terms in the equation from part C of question 1 to simplify it.

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Part B
Solve the equation for
x
.

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Part C
Using the expressions from part A of question 1, find the number of miles Gavin should ride on each of the four days.

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Part D
Add the number of miles you found for each of the four days. Does it come to 65 miles?

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Part E
What does your result in part D mean?

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Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

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