I'm confused

Question

How many gallons of a 20 % antifreeze solution and a 10 % antifreeze solution must be mixed to obtain 15 gal of a 18 % antifreeze solution? Round to the nearest gallon, if necessary.

Answer 1

Create a table:

AMOUNT:             PERCENT:                TOTAL:

10%             X                         .1                         .1X

20%           15-X                      .2                       .2(15-X)

TOTAL          15                      .18                   15*.18=2.7  

 

Notice that the first two rows must add up to equal the third (total) row.

Now we want the third (total) columns to add up and equal 2.7:

.1X+.2(15-X)=2.7

.1X+3-.2X=2.7

X=3

 

So we want 3 gallons of the 10% solution and 12 gallons of the 20% solution to have 15 gallons of 18% solution.