# Problem of the Day: 3/11/13

Two positive integers have a sum of 52. If their greatest common factor is 4, what is the least possible positive difference between the numbers?

Solution to yesterday’s problem:

If Carlo needs two cans of paint to coat three walls, then his rate of “paint usage” is $\frac{2}{3}$ cans per wall. If he needs to paint eight 4-walled rooms, he has to paint 32 walls total. He also needs to paint two coats per wall, which is equivalent to painting 32 x 2 = 64 walls total. Using the rate mentioned above, we can write

$\frac{2}{3}\times64$

to represent the number of cans of paint he needs. This evaluates to $\frac{128}{3}$, or $42\frac{2}{3}$. Remember that Carlo couldn’t very well buy two-thirds of a can of paint, so we round up to 43 cans.