Question

A scientist has two solutions, which she has labeled solution A and solution B. Each contains salt. She knows that solution A is 45% salt and solution B is 85% salt. She wants to obtain 160 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?

Answer 1

First off... let's use the decimal format for the percentages, so 85% is 85/100 or 0.85 and 45% is 45/100 or 0.45 and so on

let's say the quantities of each are "a" and "b" respectively

how much salt concentration in A? well, 0.45, so for a quantity "a", that'd be 0.45a

how much satl concentration in B? well 0.85, so for a quantity "b", that'd be 0.85b

now, she wants a mixture of 160ounces with 70% concentration, or 0.7

so the mixture will have a concentration amount of salt of 160 * 0.7

$\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentrated\\ amount \end{array}\\ &-----&-------&-------\\ \textit{sol'n A}&a&0.45&0.45a\\ \textit{sol'n B}&b&0.85&0.85b\\ -----&-----&-------&-------\\ mixture&160&0.7&112.0 \end{array} \\\\\\ \begin{cases} a+b=160\implies \boxed{b}=160-a\\ 0.45a+0.85b=112\\ ----------\\ 0.45a+0.85\left( \boxed{160-a} \right)=112 \end{cases}$

solve for "a", to see how much of the 45% solution will be needed.

what about "b"?  well, b = 160 - a

Answer 2

A is the 1st solution at 45%
B is the 2nd solution at 85%
At the end we need a solution of A and B which will generate a 160 ounces at 70%:. Note that B = 160 - A

The equation will be : 0.45.A + 0.85(160 - A) = 0.7(160)

0.45A + 136 - 0.85A = 112
- 0.40A = -24 AND A = 60 ounce and B=100 once both at 70%