Solving equations (it's supposed to be easy but i don't get it)?

Question

How much water that is 102 degrees F must be mixed with 25 gal of water at 91 degrees F, so that the resulting temperature of the water will be 97 degrees F?

Thanks. I tried doiing this equation set up but i got 28.3 gal and it's supposed to be 30 gal. Help!

Answer 1

Let x = the number of gallons of 102 degree water.

The total energy (sort of) of the 91 degree water plus the total energy of the 102 degree water will equal the total energy of the 97 degree water.

(25 * 91) + (x * 102) = (25 + x) * 97

2275 + 102x = 2425 + 97x

5x = 150

x = 30

Add 30 gal