World problem solving percent mixture

Question

A chemical company makes two brands of antifreeze. The first brand is
45%
pure antifreeze, and the second brand is
70%
pure antifreeze. In order to obtain
30
gallons of a mixture that contains
55%
pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

We want a total of 30 gallons of mixture.

If we have x gallons of 45% antifreeze, we have 30-x gallons of 70% antifreeze.

The final is 30 gallons of 55% antifreeze

 

Look at the amounts of antifreeze in each:

 

0.45x + 0.7(30-x) = 0.55(30)

0.45x + 21 - 0.7x = 16.5

-0.25x = -4.5

 

x = -4.5/(-0.25) = 18 gallons of 45% antifreeze

30-x = 12 gallons of 70% antifreeze