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

Substitute the above into equation 2:
.24x + .50y = .36(100)
.24x + .50(100-x) = .36(100)
.24x + 50-.50x = 36
50-.26x = 36
-.26x = -14
x = 53.85 gallons (of 24% solution)
.
to find 50% solution substitute above into equation 1:
x+y = 100
53.85+y = 100
y = 46.15 gallons

Answer 2

x=700/13 gallons

Answer 3

x+y=100
.24x+.50y=.36(100)