SOLUTION: 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 m

Question 346645: 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?

Found 2 solutions by nerdybill, Fombitz:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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?
.
Let x = amount of 24% solution
and y = amount of 50% solution
.
From: "The chemist wants 100 gallons when complete." we get equation 1:
x+y = 100
From: "He is mixing a 24% solution with a 50% solution to get a 36% solution." we get equation 2:
.24x + .50y = .36(100)
.
Solve equation 1 for y:
x+y = 100
y = 100-x
.
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 by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Let be the amount of 24% solution.
Let be the amount of 50% solution.
Volume equation:
1.
Concentration equation:

2.
From eq. 1,

Substitute into eq. 2,

gallons
Then from eq. 1,

gallons

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