SOLUTION: A chemist is making a solution that is to be 55% chlorine. He has one solution that is 40% chlorine and another that is 65% chlorine. He wants 100 liters of the final solution. How

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Question 154253: A chemist is making a solution that is to be 55% chlorine. He has one solution that is 40% chlorine and another that is 65% chlorine. He wants 100 liters of the final solution. How much of each should he mix?
a. Choose a variable to represent the amount of the first solution. Then find the amount of the second solution to be added to make 100 liters. Now figure out how much chlorine is in each solution.
b. Write the equation.
c. Solve the equation
Found 2 solutions by checkley77, mangopeeler07:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
.65x+.45(100-x)=100*.55
.65x+45-.45x=55
.10x=55-45
.10x=5
x=5/.10
x=50 liters of 65% is needed
100-50=50 liters of 45% is needed.
proof:
.65*50+45*50=100*55
32.5+22.5=55
55=55

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
x=amount of 40%
y=amount of 65%
coefficient=percentage

40x+65y=55(x+y)
x+y=100

Plug 100 in for x+y
40x+65y=55(100)

Solve for y
y=100-x

Plug that in for y
40x+65(100-x)=55(100)
40x+6500-65x=5500

Combine like terms
-25x+6500=5500

Subtract 6500 from both sides
-25x=-1000

Divide both sides by -25
x=40

40+y=100
y=60

40L=amount of 40%
60L=amount of 65%