Chapter 03, Review Problems, Question 59

Two gasohol mixtures are available, one with 6.35% alcohol and the other with 11.28% alcohol. How many litres of the 6.35% mixture must be added to 27.9 L of the other mixture to make a final mixture containing 8.00% alcohol?

Round the answer to one decimal place.

L

The answer is 55.4 L

x - liters of the 6.35% mixture needed

6.35% = 0.0635

11.28% = 0.1128

8% = 0.08

Liters of alcohol in 6.35% mixture is 0.0635x.

Liters of alcohol in 11.28% mixture is: 0.1128 * 27.9 L = 3.147 L

We need to get 8.00% mixture:

(0.0635x + 3.147) / (27.9 + x) = 0.08

0.0635x + 3.147 = 0.8 * (27.9 + x)

0.0635x + 3.147 = 2.232 + 0.08x

3.147 - 2.232 = 0.08x - 0.0635x

0.915 = 0.0165x

x = 0.915/0.0165

x = 55.4 L