Mr. smith needs two liters of a 65% acid solution. he has a 40% solution and an 80% solution on hand with which to make the mixture. how much of each should he use? -have to setup a system of algebraic equations and solve it.

Equations

Let the number of liters of 80% acid = x

Let the number of liters of 40% acid = y

x + y = 2

80%x + 40%y = 65% * 2

Step One

multiply the 2nd given by 100

(80/100)x + (40/100)y = (65/100)*2

80x + 40y = 2*65 = 130                 (3)

Step Two

Multiply the first given equation by 80

80x + 80y = 160                             (4)

Step Three

Subtract (4) - (3)

80x + 80y = 160

80x + 40y = 130

40y = 30               Divide by 40

y = 30/40

y = 3/4 = 0.75

What you have found is that out of 2 liters, 0.75 L must be the 40% acid.

Step Four

Find the 80% volume

x + y = 2

y = 0.75 L

x + 0.75 = 2

x = 2 - 0.75

x = 1.25 L

Answers

80% Volume = 1.25 L

40% Volume = 0.75 L

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