Linear equations

Question

How many ounces of a 10% acid mixture needs to be mixed with a 30% acid mixture to get 30 ounces of a mixture that is 25% acid?

Answer 1

You have two unknown quantities, the amount of each solution. You need two independent equations to solve the system. The first equation could be the ounces of the total solution.

(1) x + y = 30

The second could be the amount of acid in the final mixture.

(2) 0.1 · x + 0.3 · y = 0.25 · 30

Take (1) solve it for x and substitute it into (2).

0.1 · (30-y) + 0.3 · y = 7.5

3 + 0.2· y = 7.5

0.2· y = 4.5

y = 22.5 and from (1) x = 7.5

Double check my algebra but this is the general method.