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 StartFraction 1 Over 4 EndFraction left-parenthesis 0.2 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

If
`c\%` is the unknown concentration of the second solution, then each mL of this solution that is used in the new one contributes
`0.01c` mL of acid.

There are 40 mL of the new solution, and one quarter is made up of 20% acid while the remaining three-quarters is made up of the
`c\%` solution - that is, 10 mL of a 20% acid solution are used, so that its contribution is 0.2(10 mL) = 2 mL of acid, while 30 mL of the
`c\%` solution are used, so it contributes
`0.01c(30\,\mathrm{mL})=0.3c\,\mathrm{mL}` of acid.

In this new solution, we want to get a concentration of 32% acid, so it should contain 0.32(40 mL) = 12.8 mL of acid. Then the total amount of acid in the new solution satisfies

`0.3c+2=12.8\implies c=36`

so the second solution has a concentration of 36%. The equation used here is the same as the first choice (a),

`30(0.36)+10(0.2)=40(0.32)`

Answer 2

A on edg

Explanation: