100% antifreeze and 50% antifreeze should be combined to make 16 quarts of 70% antifreeze mix?

Question

100% antifreeze and 50% antifreeze should be combined to make 16 quarts of 70% antifreeze mix?

Equation 1 : (# of quarts)

Equation 2 : (strength of solution)

Answer 1

x + .5y = .7(16

y = 16-x

x + .5(16-x) = .7(16)

x - .5x = .7(16) -.5(16)

.5x -=.2(16)

x = 2(.2)(16)

x = 6.4 quarts of 100%

16-6.4 = 9.6 quarts of 50%

100 is within 30 of 70

50 is within 20 of 70

30/20 = 3/2 = 1.5

9.6/6.4 = 3/2 = 1.5

one and one half times as much 50% is needed as 100%