This math topic focuses on using algebra to solve problems involving the relationships and total values of different types of coins. The problems require forming equations based on given ratios of pennies, nickels, dimes, and quarters to find their total monetary values in cents. Each scenario varies slightly by the types and relationships of coins, and asks to set up the correct algebraic equations to determine the exact amount of each coin type based on the total value and the ratios provided between the coins. Skills practiced include problem-solving, understanding ratios, and basic algebraic manipulation.

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

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Algebra with Coins - X Fraction as Many of Coin and Total - Three Coin Types - to Equations Worksheet

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Algebra with Coins - X Fraction as Many of Coin and Total - Three Coin Types - to Equations
1
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Some coins have a total value of $0.39. There are 1/2 as many Nickels as Pennies and 1/2 as many Quarters as Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= p over 2 \\ n &= q over 2 \\1p + 25q + 5n &= 39\end{align*}
b A LaTex expression showing \begin{align*}n &= p over 2 \\ q &= n over 2 \\1p + 5n + 25q &= 39\end{align*}
2
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Some coins have a total value of $0.72. There are 1/2 as many Nickels as Pennies and 1/2 as many Dimes as Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}d &= p over 2 \\ n &= d over 2 \\1p + 10d + 5n &= 72\end{align*}
b A LaTex expression showing \begin{align*}n &= p over 2 \\ d &= n over 2 \\1p + 5n + 10d &= 72\end{align*}
3
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Some coins have a total value of $0.78. There are 1/2 as many Nickels as Pennies and 1/2 as many Quarters as Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= p over 2 \\ n &= q over 2 \\1p + 25q + 5n &= 78\end{align*}
b A LaTex expression showing \begin{align*}n &= p over 2 \\ q &= n over 2 \\1p + 5n + 25q &= 78\end{align*}
4
An svg image showing a math problem
Some coins have a total value of $0.39. There are 1/2 as many Nickels as Pennies and 1/2 as many Quarters as Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= p over 2 \\ q &= n over 2 \\1p + 5n + 25q &= 39\end{align*}
b A LaTex expression showing \begin{align*}q &= p over 2 \\ n &= q over 2 \\1p + 25q + 5n &= 39\end{align*}
5
An svg image showing a math problem
Some coins have a total value of $0.65. There are 1/2 as many Dimes as Nickels and 1/2 as many Quarters as Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}d &= q over 2 \\ n &= d over 2 \\25q + 10d + 5n &= 65\end{align*}
b A LaTex expression showing \begin{align*}d &= n over 2 \\ q &= d over 2 \\5n + 10d + 25q &= 65\end{align*}
6
An svg image showing a math problem
Some coins have a total value of $0.72. There are 1/2 as many Nickels as Pennies and 1/2 as many Dimes as Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}d &= p over 2 \\ n &= d over 2 \\1p + 10d + 5n &= 72\end{align*}
b A LaTex expression showing \begin{align*}n &= p over 2 \\ d &= n over 2 \\1p + 5n + 10d &= 72\end{align*}
7
An svg image showing a math problem
Some coins have a total value of $0.98. There are 1/2 as many Dimes as Pennies and 1/2 as many Quarters as Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= p over 2 \\ d &= q over 2 \\1p + 25q + 10d &= 98\end{align*}
b A LaTex expression showing \begin{align*}d &= p over 2 \\ q &= d over 2 \\1p + 10d + 25q &= 98\end{align*}
8
An svg image showing a math problem
Some coins have a total value of $1.30. There are 1/2 as many Dimes as Nickels and 1/2 as many Quarters as Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= d over 2 \\ q &= n over 2 \\10d + 5n + 25q &= 130\end{align*}
b A LaTex expression showing \begin{align*}d &= n over 2 \\ q &= d over 2 \\5n + 10d + 25q &= 130\end{align*}