How much water must be evaporated from 32 ounces of a 7 % salt solution to make a 8% salt? solution

Question

How much water must be evaporated from 32 ounces of a 7 % salt solution to make a 8% salt? solution

Answer 1

The problem requests the answer in terms of water. Therefore the solutions must be stated in terms of water.

 

0.93(32) - x = 0.92(32 - x)

29.76 - x = 29.44 - 0.92x

0.32 = 0.08x

4 = x

 

4 ounces must be evaporated.

 

Check:

 

0.93(32) - 4 = 0.92(32 - 4)

29.76 - 4 = 29.44 - 3.68

25.76 = 25.76

Answer 2

7% of 32=2.24 oz of salt

32-2.24=29.76 oz of water

you want the 2.24 oz of salt to be an 8% solution

8% of what is 2.24 ?

8%*n=2.24

0.08n=2.24

8n=224

n=224/8

n=28 oz

28 oz of solution, 2.24 oz of which is salt

28-2.24=25.76 oz of water

you originally had 29.76 oz of water and now you have 25.76 oz of water

29.76-25.76=4 oz of water must be evaporated

2.24 oz of salt+25.76 oz of water gives 28 oz of solution, 2.24 oz of which is salt

2.24/28=0.08=8%