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}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blccclll%7D%0A%26amount%26concentration%26%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Aconcentrated%5C%5C%0Aamount%0A%5Cend%7Barray%7D%5C%5C%0A%26-----%26-------%26-------%5C%5C%0A%5Ctextit%7B5%5C%25%20alloy%7D%26x%260.05%260.05x%5C%5C%0A%5Ctextit%7B30%5C%25%20alloy%7D%26y%260.30%260.3y%5C%5C%0A-----%26-----%26-------%26-------%5C%5C%0Amixture%26100%260.15%2615%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0Ax%2By%3D100%5Cimplies%20%5Cboxed%7By%7D%3D100-x%5C%5C%0A0.05x%2B0.3y%3D15%5C%5C%0A----------%5C%5C%0A0.5x%2B0.3%5Cleft%28%20%5Cboxed%7B100-x%7D%20%5Cright%29%3D15%0A%5Cend%7Bcases%7D)
solve for "x"
what's "y"? well, y = 100 - x
Any number multiplied by 1 is the number. Think about it this way. If I have 1 group of 8 apples, how many apples do I have? I have 8 apples :)
23 = x - 9
x= for tune
Now plug x= "for tune" into equation 23 = x - 9.
23 = "for tune" - 9
for tune = -9 - 23 = -32