Question

Suppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?

Answer 1

Can someone explain this to me step by step.

Answer 2

im sorry the measurements i am trying to remember are to inaccurate and don't add up to the 15% A sol

Answer 3

but it would seem you would need more of the 10% sol than the 30% sol

Answer 4

Isn't there a method to solving this though

Answer 5

yes..but i dont remember all the steps

Answer 6

i think you take the 30 and use a 1 15 ratio to the 10

Answer 7

to get the 15% needed

Answer 8

\(\large {
\begin{array}{rcccccl}
&ltr(sol)&acidity&ltr(acid)
\\\hline\\
10\%&x&0.1&0.1x\\
30\%\%&y&0.3&0.3y\\
mix&10&0.15&1.5
\end{array}
\\ \quad \\\\ \quad \\ \quad \\
x+y=10\implies x={\color{brown}{ 10-y}}\qquad thus
\\ \quad \\\\ \quad \\ \quad \\
\begin{array}{rcccccl}
&ltr(sol)&acidity&ltr(acid)
\\\hline\\
10\%&{\color{brown}{ 10-y}}&0.1&{\color{blue}{ 0.1(10-y)}}\\
30\%\%&y&0.3&{\color{blue}{ 0.3y}}\\
mix&10&0.15&{\color{blue}{ 1.5}}
\end{array}\qquad thus
\\ \quad \\
{\color{blue}{0.1(10-y)+0.3y=1.5 }}
}\)