Question

HELP ME PLEASE!

Delbert needs to mix a 20% acid solution with a 50% acid solution to create
100 milliliters of a 26 % solution. How many millileters of each solution must Delbert use?

Answer: Delbert must mix

_____ milliliters of the
20% solution and

_____ milliliters of the 50% solution.

Answer 1

Explanation:

26% is (26-20)/(50-20) = 6/30 = 1/5 of the way between 20% and 50%. That means 1/5 of the solution is 50% acid.

50% acid: 1/5 · 100 mL = 20 mL

20% acid: 100 mL -20 mL = 80 mL

Delbert must mix 80 mL of 20% acid and 20 mL of 50% acid.

_____

Maybe you'd like to see an equation. Let x represent the amount of 50% acid required. Then 100-x is the amount of 20% acid needed. The amount of acid in the mix is ...

0.50(x) +0.20(100 -x) = 0.26(100)

(0.50 -0.20)x = (0.26 -0.20)100 . . . . subtract 0.20(100)

x = (0.26 -0.20)/(0.50 -0.20)×100 = 20

This last expression should look a lot like the one we started with in this answer. It shows you how you can almost write down the answer to mixture problems without a lot of work.