Question

write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
kyle is collecting pledges for a walk - a - thon. his mother has pledged a flat donation of $10, and his grandmother has pledged $1 per kilometer. if kyle 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 kyle walks
\boxed{} kilometers, his mother and grandmother will each owe $
\boxed{}.

Explanation:

Step1: Define variables

Let \( d \) be the distance Kyle walks in kilometers, \( M(d) \) be the amount his mother owes, and \( G(d) \) be the amount his grandmother owes. His mother's donation is a flat \$10, so \( M(d)=10 \). His grandmother donates \$1 per kilometer, so \( G(d)=d \).

Step2: Set equations equal

We want to find when \( M(d)=G(d) \), so set \( 10 = d \).

Step3: Find the amount owed

Substitute \( d = 10 \) into either equation. Using \( M(d) \) or \( G(d) \), we get the amount is \$10 (or \( 10 \) dollars).

Answer:

If Kyle walks \( \boldsymbol{10} \) kilometers, his mother and grandmother will each owe \$ \( \boldsymbol{10} \).