A laboratory technician at a chemical supply company needs to mix a 10% hydrochloric acid solution and a 40% hydrochloric acid solution to produce 250 milliliters of a 25% solution. Let $x$ represent the volume of the 10% solution and $y$ represent the volume of the 40% solution. Which equation correctly represents the requirement that the total amount of pure hydrochloric acid in the mixture must equal the amount of pure acid in the final solution?

A laboratory technician at a pharmaceutical company is preparing a hydrochloric acid solution for a specific chemical reaction. They need to mix a 10% solution ($x$) and a 40% solution ($y$) to produce 250 milliliters of a 25% solution. They use the following system of equations to find the required volumes:

$x + y = 250$ ${}0.10x + 0.40y = 0.25(250)$

Match each mathematical component of the system to its physical meaning in this scenario.

Interpreting Mixture Problem Equations

A quality control technician needs to mix a 10% and a 40% hydrochloric acid solution to create a specific final concentration. When setting up the system of equations to solve this, the technician should use two equations that both represent the percentage of pure acid in the solutions.

A lab technician at a manufacturing plant is mixing a 10% hydrochloric acid solution and a 40% hydrochloric acid solution to create 250 milliliters of a 25% solution. To find the required volumes, $x$ and $y$, they set up a system of equations where $x + y = 250$. The second equation, ${}0.10x + 0.40y = 0.25(250)$, represents the total amount of pure ____ in the solutions.

Setting Up Mixture Equations for Chemical Compounding