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 ofthe 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

Xis equal to three