To pay back a loan, Lauren makes 7 payments, each in the same amount. Her cousin Hilary made 5 payments, each in the same amount. Each of Hilary's payments was
$15 more than each payment Lauren made. Both cousins paid the same amount in
the end. How much did each cousin pay each time?

(a) Write an equation. Let x represent the amount of one of Lauren's payments.

(b) Solve the equation. Show your work.

(c) Check your solution. Show your work.

(d) State the solution in complete sentences.