Question 1162659
<br>
Especially if this is a problem from a beginning algebra class, then you should know how to set up and solve the problem using formal algebra.<br>
However, the whole problem can be solved mentally, if an algebraic solution is not required, and if you are good with mental arithmetic.<br>
You only need to find two ways to write 1600 as the product of two positive integers which satisfy the conditions of the problem.<br>
The first four pairs that I find are these:<br>
40 * 40 = 1600
80 * 20 = 1600
64 * 25 = 1600
32 * 50 = 1600<br>
You are looking for any two numbers in that list that differ by 24; 64 and 40 satisfy that requirement.  And the corresponding numbers 40 and 25 differ by 15, which satisfies the other condition.  So these are the numbers you are looking for.<br>
ANSWER:<br>
Originally, 40 members were going to go, paying $40 each.  When 15 members backed out, 25 members paid $64 each -- an increase of $24.<br>