Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mackenzie is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $16, and her grandmother has pledged $1 per mile. If Mackenzie walks a certain distance, the two donors will end up owing the same amount. What is that distance? How much will each donor owe? If Mackenzie walks _____ miles, her mother and grandmother will each owe $_____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Mackenzie is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $16, and her grandmother has pledged $1 per mile. If Mackenzie walks a certain distance, the two donors will end up owing the same amount. What is that distance? How much will each donor owe?   If Mackenzie walks _____ miles, her mother and grandmother will each owe $_____.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables: let x be the number of miles Mackenzie walks, and let y be the amount each donor will owe. According to the problem, Mackenzie's mother will owe a flat $16, and her grandmother will owe $1 per mile. We can set up the following equation based on the information given:  Mother's pledge: y = 16 (since it's a flat donation) Grandmother's pledge: y = 1 * x (since it's $1 per mile)  Now we have a system of equations: y = 16 y = x  Since both expressions equal y, we can set them equal to each other to find the value of x.Set Up Equations: Set the two equations equal to each other to solve for x: 16 = x  This means that Mackenzie must walk 16 miles for her mother and grandmother to owe the same amount.Solve for x: Now we know the number of miles (x), we can find out how much each donor will owe (y). Since y = x and x = 16: y = 16  So each donor will owe $16.

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