Question

How many gallons of gasoline that is 5% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 3% ethanol?

Answer 1

Answer:

$V_1= 3000 gal$

Explanation:

We have 3 solutions:

• Solution 1 (with ethanol)
• Solution 2 (no ethanol)
• Final solution

$V_f=V_1 + V_2$

and for the ethanol:

$V_f*0.03=V_1*0.05 + V_2*0$

$V_f=V_1 \frac{5}{3}$

Combining:

$V_1 \frac{5}{3}=V_1 + V_2$

$V_1 \frac{2}{3}= V_2$

$V_1= \frac{3}{2} V_2$

If V2=2000 gal:

$V_1= \frac{3}{2} 2000 gal$

$V_1= 3000 gal$