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Travka [436]
3 years ago
12

A metallugarist has an alloy with 6% titanium and an alloy with 20% titanium. He needs 100 grams of an alloy with 13% titanium.

How much of each alloy should be mixed to attain the 100 grams of alloy with 13% titanium?
Mathematics
1 answer:
dsp733 years ago
4 0
\bf \begin{array}{lccclllll}
&amount(g)&\textit{\% of titanium}&\textit{grams of titanium}\\
&-----&-----&-------\\
\textit{6\% alloy}&x&0.06&0.06\cdot  x\\
\textit{20\% alloy}&y&0.2&0.2\cdot  y\\
----&-----&-----&-----\\
mixture&100&0.13&100\cdot 0.13\to 13
\end{array}

so.. .whatever those amounts are, of "x" and "y", for the mixture,
they must add up to 100 grams, or x + y = 100

and the titanium percentage of that sum, must yield a 13 grams of titanium on those 100 grams

thus \bf \begin{cases}
x+y=100\to y=\boxed{100-x}
\\\\
0.06x+0.2\boxed{y}=13
\end{cases}

do the substitution, and solve for "x",

what's "y" amount?  well, y = 100 - x
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