Question

Jon and Brantley are saving up to go on a trip together at the end of the summer. Jon had $95 at the beginning of the summer and makes $50 a day mowing lawns. Brantley only had $5 at the beginning of the summer, but he is helping his uncle who is paying him $65 a day to help in his mechanic shop. Write a system of equations to represent this situation. Then use the substitution method with that system to determine after how many days of working will they have the same amount of money. On that day how much money will they each have?

Answer 1

In 6 days they will both have $395.

Explanation:

Jon's equation is 95 + 50x = y where x is the number of days he earns $50 and y is the total amount of money for the summer.

Brantley's equation is 5 + 65x = y where x is the number of days he earns $65 and y is the total amount of money for the summer.

Substitute by setting each equation equal to each other.

95+50x = 5 + 65x

95 - 5 +50x = 5 - 5 + 65x

90 + 50x = 65x

90 + 50x-50x = 65x-50x

90 = 15x

6 = x

On day 6, they will have the same money.

They will have 95 + 50(6) = 95 + 300 = $395.