Question

A metallurgist has an alloy with 5% titanium and an alloy with 30% titanium. He needs 100 grams of an alloy with 15% titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with 15% titanium?

Answer 1

let us convert the percentages to decimal format first.. so 5% is just 5/100 or 0.05 and 15% is just 15/100 or 0.15

so hmmm, so, let's say it needs "x" amount and "y" amount of each respectively, so, whatever "x" and "y" are, they must add up to 100, and whatever their concentration is, must add up to what the mixture yields

thus


`\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentrated\\ amount \end{array}\\ &-----&-------&-------\\ \textit{5\% alloy}&x&0.05&0.05x\\ \textit{30\% alloy}&y&0.30&0.3y\\ -----&-----&-------&-------\\ mixture&100&0.15&15 \end{array} \\\\\\ \begin{cases} x+y=100\implies \boxed{y}=100-x\\ 0.05x+0.3y=15\\ ----------\\ 0.5x+0.3\left( \boxed{100-x} \right)=15 \end{cases}`

solve for "x"

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