Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a ​15% hydrochloric acid solution. Find the amount of 16​% solution and the amount of ​8% solution she should mix to get this solution.

Answer 1

8x + 16y = 16(32)

8x + 16(32-x) = 15(32)

8x + 16(32) - 16x= 15(32)

8x = 32

x = 4

y = 32-4 = 28 ounces of 16% solution mixed with 4 ounces of 8% solution gives 32 of 15%

15 is much closer to 16 than to 8, so you know you need much more of 16 than of 8. It's exactly 7 times closer, so you want 7 times more of 16% than of 8%

Answer 2

x = ounces of 16% solution

32-x = ounces of 8% solution

32 = total ounces of 15% solution:

0.16x + (32-x)*0.08 = 32(0.15)

0.16x + 2.56 - 0.08x = 4.8

0.08x = 2.24x

x = 28

28 ounces of 16% solution