Question

How many liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin? Round the answer to the nearest hundredth if necessary.


Original (L)
Added (L)
New (L)
Amount of Glycerin
0.96
x
0.96 + x
Amount of Solution
12
x
12 + x

0.18 liter
1.14 liters
1.92 liters
2.10 liters

Answer 1

Let x = liters of pure glycerin added.

Initial glycerin = 0.08·12 = 0.96 L. After adding, glycerin = 0.96 + x and total solution = 12 + x. Set up:

0.96 + x = 0.16(12 + x)

0.96 + x = 1.92 + 0.16x
0.84x = 0.96
x = 0.96/0.84 = 8/7 ≈ 1.142857

Rounded to the nearest hundredth: 1.14 liters.