Applications involving mixtures... I am not sure how to set this up

Question

Ethanol fuel mixtures have “E” numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10% ethanol and 90% gasoline. How much E5 should be mixed with 5000 gal of E10 to make an E9 mixture?

Answer 1

E5 contains 5% ethanol and 95% gasoline

 

E10 contains 10% ethanol and 90% gasoline

 

E9 contains 9% ethanol and 91% gasoline

 

X is the amount of E5

 

0.05X + 0.10*5000 = 0.09*(X+5000)

 

5X + 10(5000) = 9(X + 5000)

 

5X + 50000 = 9X + 45000

 

0 = 9X + 45000 - 5x - 50000

 

0 = 4x - 5000

 

5000 = 4x

 

x = 5000/4 = 2500/2 = 1250