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Algebra with Coins - N,M Coins of A,B Type and Reversed - Two Coin Types - to Equations

Level 1

This math topic focuses on constructing and solving algebraic equations based on scenarios involving different coin types. It teaches how to express the total values of coins through equations, considering various arrangements of two coin types and their summed values. Each problem presents two scenarios — different amounts of two specific coin types, such as nickels and pennies, or quarters and nickels — leading to two equations that assist in solving for the quantities of each coin type. The problems progress by exploring different coin combinations and value totals, integrating basic algebra with monetary concepts.

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

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Algebra with Coins - N,M Coins of A,B Type and Reversed - Two Coin Types - to Equations Worksheet

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Algebra with Coins - N,M Coins of A,B Type and Reversed - Two Coin Ty...
1
An svg image showing a math problem
With X Nickels and Y Pennies, some coins are worth $0.22. With Y Nickels and X Pennies they would be worth $0.14. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\5X + 1Y &= 22\\5Y + 1X &= 14\end{align*}
b A LaTex expression showing \begin{align*}\\10X + 1Y &= 22\\10Y + 1X &= 24\end{align*}
2
An svg image showing a math problem
With X Nickels and Y Pennies, some coins are worth $0.11. With Y Nickels and X Pennies they would be worth $0.7. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\25X + 1Y &= 11\\25Y + 1X &= 27\end{align*}
b A LaTex expression showing \begin{align*}\\5X + 1Y &= 11\\5Y + 1X &= 7\end{align*}
3
An svg image showing a math problem
With X Nickels and Y Pennies, some coins are worth $0.23. With Y Nickels and X Pennies they would be worth $0.19. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\5X + 1Y &= 23\\5Y + 1X &= 19\end{align*}
b A LaTex expression showing \begin{align*}\\5X + 10Y &= 23\\5Y + 10X &= 55\end{align*}
4
An svg image showing a math problem
With X Quarters and Y Nickels, some coins are worth $0.80. With Y Quarters and X Nickels they would be worth $0.40. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\25X + 5Y &= 80\\25Y + 5X &= 40\end{align*}
b A LaTex expression showing \begin{align*}\\25X + 1Y &= 80\\25Y + 1X &= 28\end{align*}
5
An svg image showing a math problem
With X Nickels and Y Dimes, some coins are worth $0.50. With Y Nickels and X Dimes they would be worth $0.55. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\25X + 10Y &= 50\\25Y + 10X &= 115\end{align*}
b A LaTex expression showing \begin{align*}\\5X + 10Y &= 50\\5Y + 10X &= 55\end{align*}
6
An svg image showing a math problem
With X Quarters and Y Nickels, some coins are worth $0.55. With Y Quarters and X Nickels they would be worth $0.35. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\25X + 1Y &= 55\\25Y + 1X &= 27\end{align*}
b A LaTex expression showing \begin{align*}\\25X + 5Y &= 55\\25Y + 5X &= 35\end{align*}
7
An svg image showing a math problem
With X Dimes and Y Quarters, some coins are worth $0.55. With Y Dimes and X Quarters they would be worth $0.85. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\10X + 25Y &= 55\\10Y + 25X &= 85\end{align*}
b A LaTex expression showing \begin{align*}\\10X + 1Y &= 55\\10Y + 1X &= 13\end{align*}
8
An svg image showing a math problem
With X Pennies and Y Nickels, some coins are worth $0.13. With Y Pennies and X Nickels they would be worth $0.17. What equations would help us solve for X and Y?
a A LaTex expression showing \begin{align*}\\1X + 10Y &= 13\\1Y + 10X &= 32\end{align*}
b A LaTex expression showing \begin{align*}\\1X + 5Y &= 13\\1Y + 5X &= 17\end{align*}