Question

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?

Answer 1

Answer:

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.