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?

QUESTION POSTED AT 01/06/2020 - 04:21 PM

Answered by admin AT 01/06/2020 - 04:21 PM

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
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