How much 14% acid solution should she add?

Question

A chemist wishes to mix a solution that is 10% acid. She has on hand 8 liters of 8% acid solution and wishes to add some 14% acid solution to obtain the desired 10% acid solution.

Answer 1

start with

8 liters of 8% acid = 0.64 liters of acid

 

add

x liters of 14% acid = 0.14x liters of acid

 

result is

8+x liters of 10% acid = 0.10(8 + x) liters of acid

 

 

 

The amounts of acid must add up

0.64 + 0.14x = 0.80 + 0.10x

 

mult. both sides by 100

64 + 14x = 80 + 10x

 

subtract 64 from both sides

14x = 16 + 10x

 

subtract 10x from both sides

4x = 16

 

divide both sides by 4

x = 4 liters

 

 

answer the question:

     She should add 4 liters of 14% acid

 

 

CHECK YOUR WORK (let x = 4)

 

start with
8 liters of 8% acid = 0.64 liters of acid

add
4 liters of 14% acid = 0.56 liters of acid

result is
12 liters of 10% acid = 1.20 liters of acid

 

The amounts of acid must add up
0.64 + 0.56 = 1.20 CHECK!