Chemical company makes two brands of anti-freeze the first brand is 60% pure anti-freeze and the second brain is 80% pure anti-freeze in order to obtain 40 gallons of a mixture that contains 75% pure anti-freeze how many gallons of each brand of antifreeze must be used

We have 60% and 80% antifreeze.  We need 40 gallons of 75%

We set up 2 equations:  where S = 60% and E = 80%

A) S + E = 40

B) .60S + .80E = (.75 * 40)  Multiplying A) by -.8

A) -.8S -80E = -32 Then adding this to B:

B) .60S + .80E = 30

-.2S = -2

S = 10

We will need 10 gallons of 60 % antifreeze and according to equation A) we will need 30 gallons of 80%  antifreeze.

Source: https://www.1728.org/mixture.htm

Step-by-step explanation:

(x+3)(x+7)

step-by-step explanation: