I need help solving this word problem

Question

A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 140 gallons of a mixture that contains 85% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

x represents amount of 70%

140 - x represents amount of 95%

0.70x + 0.95(140 - x) = 0.85(140)

Can you solve for x and answer?

Answer 2

First, write down the initial component concentrations: 70% 95%

\ /

Next, write down the resulting concentration: 85%

/ \

Subtract the concentrations diagonally: 10% 15%

(95%-85%) (85%-70%)

This shows that the resulting concentration will be made up of 1.5 times more of the 95% concentration than the 70% concentration: 15%/10% = 1.5.

Let x = gals of 70% concentration used

y = gals of 95% concentration used---> y = 1.5x

x + y = 140

x + 1.5x = 140

2.5x = 140

x = 140/2.5

x = 56

x + y = 140

y = 140 - x

y = 140 - 56

y = 84

Therefore, we will have to use 56 gals of the 70% concentration and 84 gals of the 95% concentration.

Hope this helps!