Linear Equations Word Problems

A chemist has two solutions of $NaCl$. The first solution has a concentration of $3M$ and the second has a concentration of $5M$. If the chemist mixes $x$ liters of the first solution with $y$ liters of the second solution to obtain a $4M$ solution, what is the equation representing this situation?

A solution contains $H_{2}SO_{4}$ at a concentration of $0.2M$. If $x$ liters of this solution are mixed with $y$ liters of pure water, the resulting concentration is $0.1M$. Which equation represents this scenario?

If a chemist has a solution of $KCl$ with a concentration of $1.5M$ and adds $4$ liters of water, the concentration becomes $1M$. What was the initial volume of the $KCl$ solution?

A $2M$ solution of $Ba(OH)_{2}$ is diluted to a final volume of $10$ liters with water. If $x$ liters of the $2M$ solution is used, what equation represents the concentration after dilution?

A laboratory has an initial $HCl$ solution of concentration $0.5M$. After adding $3$ liters of $H_{2}O$, the concentration drops to $0.4M$. What was the original volume of the $HCl$ solution?

A chemist needs to prepare $20$ liters of a $0.1M$ solution of $NaOH$. If $x$ liters of a $0.5M$ solution is used, what equation can be formed to find $x$?

A scientist has a solution of $CaCl_{2}$ at a concentration of $1M$. If she adds $4$ liters of a $0.5M$ solution, what will be the concentration of the resulting mixture in $x$ liters?

A mixture of $NH_{3}$ and $HCl$ produces $NH_{4}Cl$. If $x$ liters of $NH_{3}$ at $0.3M$ is mixed with $y$ liters of $HCl$ at $0.5M$, what is the equation for the concentration of $NH_{4}Cl$ formed?

A chemist has $x$ liters of a $3M$ solution and mixes it with $y$ liters of a $1M$ solution to create $10$ liters of a $2M$ solution. What equation represents this mixture?

A laboratory has a solution of $KNO_{3}$ at a concentration of $0.4M$. After adding $5$ liters of a $0.2M$ solution, the concentration becomes $0.3M$. What was the initial volume of the $KNO_{3}$ solution?