SOLUTION: I've tried and tried to do this problem with no success so here it is: A solution of gasoline and oil used for a gas powered weed trimmer is 8% oil. How much gasoline must be adde

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Question 29475: I've tried and tried to do this problem with no success so here it is:
A solution of gasoline and oil used for a gas powered weed trimmer is 8% oil. How much gasoline must be added to 3 gallons of this solution to obtain a new solution that is 5% oil? I set it up like this but I know this is wrong.
0.08X + 0.05(3+x)= 0.05(3) It comes up to 0
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
I sympathise
If you don't get on the right track it can lead you in never ending circles
I try to write formulas that say exactly what the words say, only in algebra
I want a symbol for oil. O looks too much like zero, so
let Q = gallons of oil in the mixture
notice the amount of oil never changes in this problem
let G = gallons of gasolione I started out with
let X = gallons of gasoline I need to add to satisfy problem
now I can write equations
[1]
that's what the 1st sentence says
there are 3 gallons of this solution, so
[2]
now I have to add gasoline to make a new solution that is 5%
[3]
Q, the amount of oil doesn't change
I can substitute [2] direcly into [1]

solve for Q

substitute this value for Q in [2]

now use these values to solve for X in [3]

so, I have to add 1.8 gallons of gasoline to the mixture to get 5% oil
check
[3]

OK
another thing to check is, if you have 3 unknowns, you need 3 equations
if I didn't have 3 equations, I'd keep looking until I found them