How many gallons?

Question

How many gallons of a 80​% antifreeze solution must be mixed with 100

gallons of 20​% antifreeze to get a mixture that is 70​% antifreeze? Use the​ six-step method.

Answer 1

.8x +.2(100) = .7(100+x) where x is the amount of 80% needed

.8x +20 =70 +.7x

.8x - .7x = 70-20

.1x =50

x= 500 gallons of 80%

check the answer

.8(50) +.2(100) = .7(600)

400 +20 = 420

80% is within 10 of 70%

20% is within 50 of 70%

that's 5 times closer for 80%

you need 5 times as much 80% as 20%

so 5 times 100 = 500 gallons of 80%