Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ 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? $\newline$ If Mackenzie walks _ miles, her mother and grandmother will each owe $\$$ _.

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Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

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?

\newline

If Mackenzie walks _____ miles, her mother and grandmother will each owe

\$

_____.

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: $\newline$ Mother's pledge: $y = 16$ (since it's a flat donation) $\newline$ Grandmother's pledge: $y = 1 \times x$ (since it's $\$1$ per mile) $\newline$ Now we have a system of equations: $\newline$ $y = 16$ $\newline$ $y = x$ $\newline$ 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 $x = 16$ : $\newline$ $y = 16$ $\newline$ So each donor will owe $\$16$ .