Let's say q is the number of quarts he needs for the inside, which is what we're trying to find.
Then he needs 19 more quarts for the outside, so q + 19 is the number he needs for the outside.
Total, he needs 107 quarts to paint the inside and outside.
q + q + 19 = 107
2q = 107 - 19 = 88
q = 44 (quarts)
