A chemist wants to make 54 ml of a 17% acid solution by mixing a 10% acid solution and a 19% acid solution. How many milliliters of each solution should the chemist use?

Question

A chemist wants to make 54 ml of a 17% acid solution by mixing a 10% acid solution and a 19% acid solution. How many milliliters of each solution should the chemist use?

Answer 1

Let x represent the amount (in ml) of the 10% acid solution

and y represent the amount (in ml) of the 19% acid solution

So, for volume, x + y = 54 ------> in other words y = 54 - x

Also, for acidity, 0.10x + 0.19y = 0.17(54)

Substitute y ---> 0.10x + 0.19(54-x) = 9.18

Distribute --------> 0.10x + 10.26 - 0.19x = 9.18

Combine terms -------> -0.09x +10.26 = 9.18

Continue to solve for x ----------> -0.09x = 9.18 - 10.26

-0.09x = -1.08

Divide both sides by -0.09 ----------> x = -1.08/-0.09 = 12 ml of the 10% acid solution

To solve for y, recall that y = 54 - x = 54 - 12 = 42 ml of the 19% acid solution

Answer 2

0.19x + 0.10(54 - x) = 0.17(54)

Can you solve for x and answer?