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.
