Maya has a lot of 50% sugar syrup. Genna has 20 quarts of a 20% sugar syrup. The girls want to use all Genna's syrup and some of Maya's syrup to make a 40% sugar syrup. How much of Maya's syrup should they use?

To solve the problem we must establish 2 equations, to solve for the 2 unknown.

let x be the amount of Maya's sugar syrup

y be the amount of mix sugar syrup

using overall mass balance

x + 20 = y

sugar balance

0.5x + 20 (0.20) = 0.40y

then solve the equation simultaneously

x = 40 quarts of Maya's syrup should they use