Question

A gas station owner has 30 gallons of gasoline for which he charges $3.03 per gallon and
some for which he charges $3.74 per gallon. How many gallons of the $3.74 brand must the owner mix in to produce gasoline that costs $3.28 per gallon?

Answer 1

Type A is 3.03/gal. Type B is 3.74/gal. The percentage of total gallons (30+x, where x is number of gallons of type B) of each type varies directly with how much that type's price contributes to the final price.
3.28=3.03*(30/(30+x))+3.74*(x/(30+x)).
3.28=90.9/(30+x)+3.74x/(30+x)
3.28=(90.9+3.74x)/(30+x)
3.28(30+x)=90.9+3.74x
98.4+3.28x=90.9+3.74x
7.5=.46x
7.5*.46=x=your answer=(15/2)(46/100)=23*15/100=3.45 gallons

Answer 2

this doesn't feel right, it should be checked. I was thinking the answer should be around 10

Answer 3

looks good to me thanks

Answer 4

oh, I see where I went wrong thinking I wasn't right (lolwut). My approximation is 10/3, which comes out nicely to the answer I got algebraically