Respuesta :
We have to blend two mixtures of ethanol (E7 and E10) to make an E9 mixture.
We know that the amount of E10 mixture is 4000 gal.
Let x be the amount of E7 mixture.
As we have x gallons of E7 and 4000 gallons of E10, the volume of the E9 mixture will be (x+4000).
The volume of ethanol in the E7 mixture will be 0.07*x gallons.
The volume of ethanol in the E10 mixture is 0.1*4000 = 400 gallons.
The volume of ethanol in the E9 mixture will be 0.09*(x+4000) gallons.
As the sum of the ethanol volume in the E7 and E10 mixtures has to be equal to the ethanol in the E9 mixture, we can write:
[tex]0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000)[/tex]We can use this equation to solve for x:
[tex]\begin{gathered} 0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000) \\ 0.07x+400=0.09x+0.09\cdot4000 \\ 0.07x+400=0.09x+360 \\ 0.07x-0.09x=360-400 \\ -0.02x=-40 \\ x=\frac{40}{0.02} \\ x=2000 \end{gathered}[/tex]Then, the volume of the E7 mixture has to be 2000 gallons.
Answer: 2000 gallons of E7 mixture.
