Question

Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?

Answer 1

Let x be the number of gallons of 24% solution and y be the number of gallons of the 50% solution.

He wants 100 gallons in total. So x + y = 100.

Let's convert the percentages to decimals. Your other equation will be 0.24x + 0.50y = 0.36*100, or
0.24x + 0.5y = 36.