Mixture problem of ethanol 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. The numbers indicate the percentage of ethanol in the mixture by volume. 5000 gal of E10 contains 500 gal ethanol and 4500 gal gasoline. 0.05x+500 = 0.09(x+5000) Is this right?

Let $x$ be the volume of E5 to be mixed, then the ethanol in the mixture is $$0.05x+0.1\cdot 5000$$ To obtain E9, this number should be equal to $0.09(x+5000)$. So you have to solve the equation $$0.05x+0.1\cdot 5000=0.09(x+5000)$$ that is $0.04x=0.01\cdot 5000$ and $x=1250$.