Question

How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze? Use the six-step method.

Answer 1

405 gallons

Explanation:

Let it be that the amount of gallons of a 70% antifreeze solution is x, when a mixture that is 60 percents of antifreeze is placed in y gallons

x+90=y - the equation of dependence between solutions

The amount of antifreeze in the first one is x/100*70= 0.7x (in gallons), in the second solution (15percents) antifreeze is 90/100*15=13.5 (in gallons).

In the mixture we should get there will be y/100*60=0.6y - gallons of antifreeze

0,7x+13.5=0.6y

We have two equations x+90=y and 0,7x+13.5= 0.6y

0.6x+54=0.6y

0.7x+13.5=0.6y

0.7x+13.5-0.6x-54= 0.6y-0.6y

0.1x-40.5=0

x=405- the answer

p.s. sorry, I don't know what the six-step method is. But the answer is right.