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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Perry is collecting pledges for a walk-a-thon. His mother has pledged a flat donation of , and his grandmother has pledged per mile. If Perry walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe? What is that distance?Perry's mother and grandmother will each owe _____ if he walks _____ miles.
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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Perry is collecting pledges for a walk-a-thon. His mother has pledged a flat donation of , and his grandmother has pledged per mile. If Perry walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe? What is that distance?Perry's mother and grandmother will each owe _____ if he walks _____ miles.
- Define Variables: Let's define the variables.Let be the number of miles Perry walks.Let be the amount of money each donor will owe.
- Mother's Pledge: Write the equation for Perry's mother's pledge.Perry's mother pledged a flat donation of , so regardless of the distance Perry walks, she will owe .
- Grandmother's Pledge: Write the equation for Perry's grandmother's pledge.Perry's grandmother pledged per mile, so the amount she will owe is times the number of miles Perry walks.
- Set Equations Equal: Set the two equations equal to each other to find the distance at which both donors will owe the same amount.Since both 's represent the amount owed and they are equal:
- Solve for x: Solve for x to find the number of miles Perry must walk.Divide both sides of the equation by to isolate x:
- Find Amount Owed: Determine the amount each donor will owe when Perry walks miles.Since we have found that , we can substitute this value into either equation to find . We'll use Perry's grandmother's pledge equation:
