Algebra, Please help me

Question

A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 70% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

You know the amounts of the two components add to 150 gallons, so the amounts can be expressed as x and (150-x).

 

0.65 x + 0.95 (150-x) = 0.70 (150)

0.65 x + 142.5 - 0.95 x = 105

 

37.5 = 0.3 x

 

125 = x

125 gallons of the 65% solution + 25 (150 - 125) gallons of the 95% solution = 150 gallons of the 70% solution.

Check:  125 (0.65) + 25 (0.95) = 150 (0.70).  81.25 + 23.75 = 105.00.  There are 105 gallons of antifreeze in the solution.  105 is 70% of 150.

Answer 2

65%x+95%(150-x)=70%(150)

0.65x+142.5-0.95x=105

-0.3x+142.5=105

142.5-105=0.3x

37.5=0.3x

375=3x

x=375/3

x=125 gallons of the 65% mixture and 25 gallons of the 95% mixture