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.
□ l of 5% solution
□ l of 25 % solution

Explanation:

Step1: Set up total volume equation

The sum of the two solutions equals 10 L:
$x + y = 10$

Step2: Set up solute amount equation

The total pure sodium chloride from both solutions equals the solute in the final 10% solution:
$0.05x + 0.25y = 0.10 \times 10$
Simplify the right-hand side:
$0.05x + 0.25y = 1$

Step3: Solve for one variable

From Step1, isolate $x$:
$x = 10 - y$

Step4: Substitute and solve for $y$

Substitute $x=10-y$ into the equation from Step2:
$0.05(10 - y) + 0.25y = 1$
Expand and simplify:
$0.5 - 0.05y + 0.25y = 1$
$0.5 + 0.2y = 1$
$0.2y = 1 - 0.5$
$0.2y = 0.5$
$y = \frac{0.5}{0.2} = 2.5$

Step5: Solve for $x$

Substitute $y=2.5$ into $x=10-y$:
$x = 10 - 2.5 = 7.5$

Answer:

7.5 L of 5% solution
2.5 L of 25% solution