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serious [3.7K]
2 years ago
7

A chemist wants to make 100 liters of a 44% acid solution. She has solutions that are 20% acid and 60% acid.

Mathematics
1 answer:
alexgriva [62]2 years ago
7 0

the first solution is 20% acid, and say we'll be using "x" liters, so how many liters of just acid are in it?  well 20% of "x" or namely 0.2x.  Likewise for the 60% acid solution, if we had "y" liters of it, the amount of only acid in it is 0.6y.

\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ \textit{1st solution}&x&0.20&0.2x\\ \textit{2nd solution}&y&0.60&0.6y\\ \cline{2-4}&\\ mixture&100&0.44&44 \end{array}~\hfill \begin{cases} x+y=100\\\\ 0.2x+0.6y=44 \end{cases}

x+y=100\implies y=100-x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.2x+0.6(100-x)=44} \\\\\\ 0.2x+60-0.6x=44\implies -0.4x+60=44\implies -0.4x=-16 \\\\\\ x=\cfrac{-16}{-0.4}\implies \boxed{x=40}~\hfill \boxed{\stackrel{100-40}{y=60}}

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Answer:

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Combine like terms

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Now plug in the solutions Note: it is easier if you have all decimals or all fractions (-1/10=-.1

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I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3
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There are five nickels.

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Then, we have three equations with four unknowns:

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(3) 2<em>y</em> = 3<em>z</em>

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