A rappelling club charters a bus for a trip to the mountains for $540. To lower the bus fare per person, the club invites some hikers on the trip. After 7 hikers join the trip, the bus fare per person decreases by $7. How many members of the rappelling club are going on the trip?

20 members of the rappelling club are going on the trip

Explanation:

Total cost of the trip is $540.

If only one person goes, the cost is $540.

We can make the total number of people going x since we are not given.

Therefore, each member would pay (540/x)

We can also rep 7 with non members since the number is given as 7

Total people going = Members + non members.

Therefore, the cost per person is now (540/x+7).

Problem.

540/x - 540/x + 7 = 7

Multiply each with lowest common denominator.

When you expand, you get

540 (x+7) - x (540) / x (x+7) = 7

Simplify multiplication.

540x+3780-540x=7 (x^2+7x)

Combine like terms

540x-540x+3780=7x^2+49x

3780=7x^2+49x

7x^2+49x-3780 = 0

When we divide through by 7, we have

x^2+7x-540

Factorize, we have

(x^2+27x) - (20x-540) = 0

x (x+27) - 20 (x+27) = 0

(x-20) (x+27) = 0

x is therefore 20 or - 27

Since we know - 27 cannot be a reasonable answer hence must be excluded.

The exact number of the people going on the trip is 20.