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Linear Equations Word Problems

This worksheet covers Linear Equations Word Problems, which is part of the Lines Destroyer module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Equation From Two Points

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Linear Equations Word Problems

Lines Destroyer • SAT Math Destroyer Crash Course

Set 2 — Mastery

A chemist is mixing a solution that contains $x$ grams of solute in $y$ liters of solution. If the desired concentration is 10 grams per liter, what is the equation representing this relationship?

$y = \frac{x}{10}$

$x = 10y$

$x + y = 10$

$x = 10 + y$

If a certain chemical reaction produces $z$ grams of product for every $2x$ grams of reactant used, what is the linear equation representing this relationship?

$z = 2x$

$x = \frac{z}{2}$

$z + 2x = 0$

$2z = x$

A laboratory has $p$ grams of a solution that is 25% acid. If the chemist adds $q$ grams of pure acid, which results in a final concentration of 40% acid, what equation represents this situation?

$0.25p + q = 0.4(p + q)$

$0.4p + q = 0.25(p + q)$

$p + q = 0.25$

$0.25p + 0.4q = 1$

A solution is prepared by mixing $x$ liters of a 30% solution with $y$ liters of a 50% solution to obtain a 40% solution. Which equation correctly represents this mixture?

$0.3x + 0.5y = 0.4(x + y)$

$0.4x + 0.3y = 0.5(x + y)$

$x + y = 40$

$0.3x + 0.4y = 0.5$

A scientist needs to dilute a $H_{2}SO_{4}$ solution from 70% to 20%. If the final volume should be $V$ liters, how much pure water $W$ (in liters) must be added to achieve this dilution?

$W = V - 0.7V$

$W = 0.7V - 0.2V$

$W = V(0.7 - 0.2)$

$W = V(0.2 - 0.7)$

In a reaction, $A$ is consumed at a rate of $2x$ grams per hour and $B$ is consumed at a rate of $3y$ grams per hour. If the total consumption rate is 60 grams per hour, which equation represents their relationship?

$2x + 3y = 60$

$2x - 3y = 60$

$3x + 2y = 60$

$x + y = 60$

A student is preparing a $NaCl$ solution by mixing $x$ grams of $NaCl$ with $y$ liters of water. If the desired concentration is 5 grams per liter, what is the equation to represent this concentration?

$x = 5y$

$y = \frac{x}{5}$

$x + y = 5$

$x = 5 + y$

A factory produces $m$ grams of a chemical compound. If the production rate is $R$ grams per hour, how many hours $H$ will it take to produce $m$ grams?

$H = \frac{m}{R}$

$H = mR$

$H = \frac{R}{m}$

$H = m + R$

An experiment requires $x$ grams of $CaCO_{3}$ and $y$ grams of $HCl$ . The reaction produces $z$ grams of $CaCl_{2}$ . If the stoichiometry of the reaction is $1:2:1$ , how can we express this relationship in an equation?

$x + 2y = z$

$1x + 1y = z$

$z = x + 2y$

$x + y + z = 0$

10.

To achieve a specific molarity, a chemist needs to dissolve $x$ grams of $KCl$ in $y$ liters of solution. If the desired molarity is 0.5 mol/L and the molar mass of $KCl$ is 74.55 g/mol, which equation represents this relationship?

$x = 0.5 \times y \times 74.55$

$y = \frac{x}{0.5 \times 74.55}$

$x + y = 0.5$

$x = 0.5 + y$

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