Need to determine how many gallons of gasoline need to be added

Question

A two cycle engine mechanic has 5 gallons of fuel mixture that is 85% gasoline and 15% oil. How many gallons of gasoline should be added to form a fuel mixture that is 97% gasoline and 3% oil  

 

 

could you you help me set up this problem and solve it

Answer 1

So currently you have .85*5 = 4.25 gallons of gas and .75 gallons of oil.

 

I am adding pure gas. let's call that g.

So (4.25 + g) is the new amount of gas and 5+g is the total amount of liquid. So

 

(4.25 + g)/(5+g) = .97....cross multiply to get

4.25 + g = 4.85 + .97g

        .03g = .6

            g = 20

 

So if you add 20 gallons of pure gas, you get 24.25 gallons of gas and 25 gallons of liquid leaving .75 gallons of oil.

 

So 24.25/25 = .97 and .75/25 = .03 which are the exact requirements of the problem.
Hope this helped.