IP2 Class Test (May 2025) Q11

A sport club purchased an equipment of \$\(\)\(1500\) to be shared by a group of \(x\) members. It was agreed that each member of the group would pay an equal share of the equipment fee.

1. Write down an expression, in terms of \(x\), for the amount of money each member of the group had to pay.[1]

Three members of the group then quit the club. The club decided that it would contribute \$\(\)\(140\) from its funds and that the balance of the fee was to be shared equally by the remaining members.

2. Write down an expression, in terms of \(x\), for the amount of money each remaining member had to pay after the three members quit.[1]
3. As a result of the three members quitting, the amount each member had to pay was \$\(\)\(5\) more than the initial amount.
   Form an equation in \(x\) and show that it reduces to \(x^2 + 25x - 900 = 0\).[3]
4. Solve the equation \(x^2 + 25x - 900 = 0\).[2]
5. Find the amount of money that each member had to pay initially.[2]