Question

Use a system of equations to solve this problem. A chemist currently has two solutions of sodium chloride. One solution has a 5% concentration and the other has a 25% concentration. The chemist needs to make 10 L of a 10% sodium chloride solution. Let x = the amount of 5% solution. Let y = the amount of 25% solution. How much of each solution does the chemist need to make? Enter your answers, as decimals, in the boxes.

Answer 1

`\begin{array}{ccccllll} &amount(ltr)&\textit{acid \%}&\textit{total acidic amount(ltr)}\\ &------&------&------------\\ \textit{5\% sol'n}&x&0.05&0.05x\\ \textit{25\% sol'n}&y&0.25&0.25y\\ ------&------&------&------------\\ \textit{10\% mixture}&10&0.10&1.00 \end{array}`

so.. whatever the sum of "x" and "y" is, it must come with a 10Liter
solution of 10% or 10/100 = 0.10 acidity
thus
`\bf \begin{cases} x+y=10\\ 0.05x+0.25y=1.00\\ --------------\\ x+y=10\to x=\boxed{10-y}\\ --------------\\ 0.05(\boxed{10-y})+0.25y=1.00 \end{cases}`

solve for "y" to see how much of the 25% solution must be used,

how much "x" will it be? well x = 10 -y :)