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

1. 1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.
For given question,
Let x be the quantity ( in liters ) of glycerin added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin,
Thus,
Quantity of glycerin in 12 liters + Quantity of glycerin in x
= Quantity of glycerin in resultant mixture.
⇒ 8% of 12 + 100% of x = 16% of (12 + x )
⇒ 0.08 × 12 + x = 0.16 × ( 12 + x )
⇒ 0.96 + x = 0.16 × 12 + 0.16x
⇒ 0.96 + x = 1.92 + 0.16x
⇒ x – 0.16x = 1.92 – 0.96
⇒ 0.84x = 0.96
⇒ x = 1.143 liters
Therefore, 1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.