Question

Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the solution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c.

Which equation can be used to determine c, the unknown concentration?

30c + 10(0.2) = 40(0.32)
StartFraction 3 Over 4 EndFraction left-parenthesis c right parenthesis plus left-parenthesis StartFraction 1 Over 4 EndFraction left-parenthesis 0.2 right-parenthesis right-parenthesis equals 40 times 0.32.(c) + StartFraction 1 Over 4 EndFraction cup.(0.2) = 40(0.32)
(c)( (0.2)) = 40(0.32)
30(c)(10(0.2)) = 40(0.32)

Answer 1

The first option (30c + 10(0.2) = 40(0.32)

Answer 2

Solution 1 : 10mL with 20% acid

Solution 2 : 30mL with x% acid

Solution 3 : 40mL with 32% acid

Explanation:

Since solution 1 + solution 2 = solution 3, let us substitute the given values we have:

10(0.2) + 30(x) = 40(0.32)

2 + 30x = 12.8

To solve for the unknown concentration x, we subtract 2 from both sides:

2 + 30x - 2 = 12.8 - 2

30x = 10.8

Dividing both sides by 30:

30x/30 = 10.8/30

x = 0.36

Therefore the unknown solution is 36% acid.