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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Jennifer is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of , and her grandmother has pledged per kilometer. If Jennifer walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe? What is that distance?Jennifer's mother and grandmother will each owe _____ if she walks _____ kilometers.
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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Jennifer is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of , and her grandmother has pledged per kilometer. If Jennifer walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe? What is that distance?Jennifer's mother and grandmother will each owe _____ if she walks _____ kilometers.
- Define Variables: Let's define the variables:Let be the number of kilometers Jennifer walks.Let be the amount of money owed by each donor.We can write two equations based on the information given:Jennifer's mother's pledge: (flat donation)Jennifer's grandmother's pledge: per kilometer Now we can write the system of equations:Equation : Equation : We are told that both donors will end up owing the same amount, so we can set the two equations equal to each other to find the distance .
- Write Equations: Now we solve the system using substitution:Since from Equation , we can substitute for in Equation :Now we solve for :So, Jennifer needs to walk kilometers for both donors to owe the same amount.
- Solve System: Now that we know Jennifer walks kilometers, we can find out how much each donor will owe. We can use either Equation or Equation to find , the amount owed.Using Equation (since it's simpler):So, each donor will owe if Jennifer walks kilometers.
