Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125?

Question

Four different positive integers sum to one hundred twenty-five.  If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers.  What are the four original numbers that sum to 125?

John · Answer

If you interpret the question, you can come up with a system of equations to solve, for example:

w + x + y + z = 125
w + 4 = x - 4
3y = z/4
x - 4 = 3y

The first equation comes from the first statement that the four numbers sum to 125. The other three come from the second statement about changing the numbers to make them all equivalent. You can solve the system from here.