Answer to the Math Problem of the Week for March 11, 2014

Question: I'm thinking of 4 numbers which add up to 45. If you add 2 to one of the numbers, subtract 2 from another, divide another by 2 and multiply the last by 2, you wind up with 4 equal numbers. What numbers am I thinking of?

Answer:  5, 8, 12, and 20

a + b + c + d = 45

a + 2 = x
b - 2 = x
c / 2 = x
d * 2 = x

Solve for a, b, c, and d; substitute back into the original equation. Now you only have one variable to solve for: x.

a = x - 2
b = x + 2
c = x * 2
d = x / 2

(x - 2) + (x + 2) + (x * 2) + (x / 2) = 45

1x + 1x + 2x + .5x = 4.5x = 45

x = 10

a = 10 - 2 = 8
b = 10 + 2 = 12
c = 10 * 2 = 20
d = 10 / 2 = 5