SOLUTION: The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $3200, which was to be divided equally among the members going. Prior to the trip, 15 members dec
Question 1162699: The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $3200, which was to be divided equally among the members going. Prior to the trip, 15 members decided not to go. If the cost per person increased by $48, how many people went on the expedition? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52776) (Show Source):
A setup for solving the problem using formal algebra....
Let x be the number who went on the expedition. Then x+15 is the number that were originally going to go.
The cost per person originally was 3200/(x+15); the cost now is 3200/x.
We are told the difference between those two costs is $48:
Multiply by the common denominator x(x+15) to clear fractions:
To solve that by factoring, you need to find two integers with a difference of 15 whose product is 1000. If your mental math is good, you should find 25 and 40 work. So
Ignore the negative solution, since it makes no sense in the problem.
ANSWER: 25 people went on the trip.
CHECK:
3200/25 = 128
3200/40 = 80
128-80 = 48
You should know how to set up and solve the problem like that, using formal algebra.
But if a formal algebraic solution is not required, you can solve the problem much faster if your mental math is good.
In the original problem, you need to find two different pairs of two positive integers that give a product of 3200; you are looking to have the differences between the numbers in the two pairs equal to 15 and 48.
A bit of playing around with the numbers will find
40*80 = 3200
25*128 = 3200
The difference between 40 and 25 is 15; the difference between 80 and 128 is 48. So those numbers are the ones we want.
So originally there were 40 members paying $80 each, and in the end there were 25 members paying $128 each.
