You need $250 \mathrm{~mL}$ of a $45 \%$ alcohol solution. On hand, you have a $40 \%$ alcohol mixture. You also have a $90 \%$ alcohol mixture. How much of each mixture will you need to add to obtain the desired solution?
You will need
$\mathrm{mL}$ of the $40 \%$ solution
$\mathrm{mL}$ of the $90 \%$ solution
Answer
Final Answer: You will need \(\boxed{225 \mathrm{~mL}}\) of the 40% solution and \(\boxed{25 \mathrm{~mL}}\) of the 90% solution.
Step 1 ：Let's denote the amount of the 40% solution as x and the amount of the 90% solution as y.
Step 2 ：We know that the total volume of the solution must be 250 mL, so we can write the equation as \(x + y = 250\).
Step 3 ：The total amount of alcohol in the solution must be 45% of the total volume, so we can write the equation as \(0.4x + 0.9y = 112.5\).
Step 4 ：Solving this system of equations, we find that \(x = 225\) and \(y = 25\).
Step 5 ：Final Answer: You will need \(\boxed{225 \mathrm{~mL}}\) of the 40% solution and \(\boxed{25 \mathrm{~mL}}\) of the 90% solution.
