Algebra Word Problem

Question

Mr. White’s radiator contains 3 gals of a 50% antifreeze solution. If he wants to increase the percent of antifreeze to 60%, how much fluid should he drain from the radiator and replace it with pure antifreeze?

Answer 1

0.50(3 - x) + x = 0.60(3)

Answer 2

3 gallons of 50%

drain how much of the 50% and replace with 100% to get 3 gallons of 60%?

let that amount = x which leaves 3-x of the 50% mixed with x of 100%

(.50)(3-x) + (1.00)x = (.60)(3)

expand

1.5 -.5x + x = 1.8

combine like terms

.5x = 1.8-1.5

.5x= .3

multiply by 2

x = .6 gallons= 3/5 gallon

drain 3/5 of a gallon of 50% and replace with 3/5 of 100%

to mix the remaining 2 2/5 of 50% with 3/5 gallon of 100%

to get 3 gallons of 60%

check the answer

.5(2.4) + .6 = 1.2+.6 = 1.8 = .6(3)

100-60 = 40

60-50 = 10

40/10 = 4

Mr. White needs 4 times as much 50% as 100%

(2 2/5)/(3/5) = (12/5)/(3/5) = 12/3 = 4