Question

James needs 70 liters of 50% antifreeze. He has 30% antifreeze and 80% antifreeze avail- able. How many liters of the 30% antifreeze and how many liters of the 80% antifreeze should he mix to make the 50% antifreeze?

Answer 1

(42,28)

Explanation:

set up the problem by converting percentages to decimal

x+y=70

.30x+.80y=50(x+y)

solve for x, so minus y in order to get it x alone. equation should look like this: x=70-y

30(70-y)+80y=50(70-y+y)

solve the equation for y

y=28

plug the value of y into the equation x=70-y

x=70-28

solve for x

x=42

check the solution of (42,28)

42+28=70

30*42+80*28=50(42+28)

simplify the equations

70=70

3500=3500

the ordered pair is a solution

so James needs 42 liters of 30% antifreeze and 28 liters of 80% antifreeze.

(42,28)

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