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?

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?

anonymous · Answer

Let the first solution be denoted by "x" and the second solution be denoted by "y".
According to the first condition, x+y=100....(i)
According to the second condition, 0.24x+0.5y=(36/100)*100=36
Or, by solving (i) and (ii), we get, 12x+25y=1800 and x+y=100
Therefore, y=600/13=46.15(approx) and x=53.85(approx)