This topic focuses on solving algebraic equations involving coins. It teaches how to create and solve equations based on scenarios where different types of coins have specific ratios to one another and a given total value. For example, finding equations that can determine the quantity of pennies and quarters when there are four times as many pennies as quarters, with a combined value. This involves converting real-world problems into algebraic expressions, enhancing skills in translating verbal statements to mathematical equations and variable manipulation. These problems utilize basic concepts and introductory skills in algebra.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebra with Coins - X Times as Many of Coin and Total - Two Coin Types - to Equations Worksheet

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Algebra with Coins - X Times as Many of Coin and Total - Two Coin Types - to Equations
1
An svg image showing a math problem
Some coins have a total value of $0.87. There are 4 times as many Pennies than Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= 4q\\1p + 25q &= 87\end{align*}
b A LaTex expression showing \begin{align*}q &= 4p\\25q + 1p &= 87\end{align*}
2
An svg image showing a math problem
Some coins have a total value of $1.05. There are 2 times as many Nickels than Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= 2q\\5n + 25q &= 105\end{align*}
b A LaTex expression showing \begin{align*}q &= 2n\\25q + 5n &= 105\end{align*}
3
An svg image showing a math problem
Some coins have a total value of $0.20. There are 2 times as many Nickels than Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}d &= 2n\\10d + 5n &= 20\end{align*}
b A LaTex expression showing \begin{align*}n &= 2d\\5n + 10d &= 20\end{align*}
4
An svg image showing a math problem
Some coins have a total value of $0.20. There are 2 times as many Nickels than Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= 2d\\5n + 10d &= 20\end{align*}
b A LaTex expression showing \begin{align*}d &= 2n\\10d + 5n &= 20\end{align*}
5
An svg image showing a math problem
Some coins have a total value of $0.90. There are 2 times as many Dimes than Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= 2d\\25q + 10d &= 90\end{align*}
b A LaTex expression showing \begin{align*}d &= 2q\\10d + 25q &= 90\end{align*}
6
An svg image showing a math problem
Some coins have a total value of $0.28. There are 4 times as many Pennies than Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= 4d\\1p + 10d &= 28\end{align*}
b A LaTex expression showing \begin{align*}d &= 4p\\10d + 1p &= 28\end{align*}
7
An svg image showing a math problem
Some coins have a total value of $0.29. There are 4 times as many Pennies than Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= 4q\\1p + 25q &= 29\end{align*}
b A LaTex expression showing \begin{align*}q &= 4p\\25q + 1p &= 29\end{align*}
8
An svg image showing a math problem
Some coins have a total value of $0.09. There are 4 times as many Pennies than Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= 4p\\5n + 1p &= 9\end{align*}
b A LaTex expression showing \begin{align*}p &= 4n\\1p + 5n &= 9\end{align*}