Question

A metallurgist has an alloy with 10​% titanium and an alloy with 20​% titanium. He needs 100 grams of an alloy with 17​% titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with 17​% ​titanium?

Answer 1

$\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentration\\ amount \end{array}\\ &-----&-------&-------\\ \textit{10\% alloy}&x&0.1&0.1x\\ \textit{20\% alloy}&y&0.2&0.2y\\ -----&-----&-------&-------\\ mixture&100&0.17&17 \end{array}$

now, notice, we use the decimal format for the percent, namely 17% is 17/100 or 0.17 and so on

so....  we know, whatever "x" and "y" is, they must add up to 100 grams
thus    x + y = 100

and whatever the concentrated amount is, it must add up to 17 grams for the composition

thus   0.1x + 0.2y = 17

$\bf \begin{cases} x+y=100\implies \boxed{y}=100-x\\ 0.1x+0.2y=17\\ ----------\\ 0.1x+0.2\left( \boxed{100-x} \right)=17 \end{cases}$

solve for "x", to see how much is needed of the 10% alloy

what about "y"? well, y = 100 - x