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Algebra with Coins - Same Count of Two and Two with Four Coin Types - to Equations

Level 1

This math topic involves algebraic problem-solving related to the total value and quantity of coins. It embraces situations where the count of different types of coins (pennies, nickels, dimes, quarters) is equal or pairs of them have the same counts. The problems offer equations where the student must identify and organize terms representing the value and number of each coin type to achieve a given total monetary value. Each problem is coupled with two potential sets of equations, testing students' comprehension of variable relationships and algebraic formulation.

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

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Algebra with Coins - Same Count of Two and Two with Four Coin Types - to Equations Worksheet

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Algebra with Coins - Same Count of Two and Two with Four Coin Types - to Equations
1
An svg image showing a math problem
Some coins have a total value of $2.05 There are the same number of Pennies, Nickels, Dimes, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\n &= d\\d &= q\\1p + 5n + 10d + 25q &= 205\end{align*}
b A LaTex expression showing \begin{align*}d &= q\\q &= n\\n &= p\\10d + 25q + 5n + 1p &= 205\end{align*}
2
An svg image showing a math problem
Some coins have a total value of $1.46 There are the same number of Dimes and Quarters, and the same number of Pennies and Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= n\\p &= d\\25q + 5n + 1p + 10d &= 146\end{align*}
b A LaTex expression showing \begin{align*}d &= q\\p &= n\\10d + 25q + 1p + 5n &= 146\end{align*}
3
An svg image showing a math problem
Some coins have a total value of $0.76 There are the same number of Dimes and Quarters, and the same number of Pennies and Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}d &= q\\p &= n\\10d + 25q + 1p + 5n &= 76\end{align*}
b A LaTex expression showing \begin{align*}d &= p\\n &= q\\10d + 1p + 5n + 25q &= 76\end{align*}
4
An svg image showing a math problem
Some coins have a total value of $0.59 There are the same number of Pennies and Nickels, and the same number of Dimes and Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\d &= q\\1p + 5n + 10d + 25q &= 59\end{align*}
b A LaTex expression showing \begin{align*}n &= p\\d &= q\\5n + 1p + 10d + 25q &= 59\end{align*}
5
An svg image showing a math problem
Some coins have a total value of $1.00 There are the same number of Pennies and Nickels, and the same number of Dimes and Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\d &= q\\1p + 5n + 10d + 25q &= 100\end{align*}
b A LaTex expression showing \begin{align*}n &= q\\d &= p\\5n + 25q + 10d + 1p &= 100\end{align*}
6
An svg image showing a math problem
Some coins have a total value of $1.34 There are the same number of Pennies and Dimes, and the same number of Nickels and Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\q &= d\\1p + 5n + 25q + 10d &= 134\end{align*}
b A LaTex expression showing \begin{align*}p &= d\\n &= q\\1p + 10d + 5n + 25q &= 134\end{align*}
7
An svg image showing a math problem
Some coins have a total value of $1.64 There are the same number of Pennies, Nickels, Dimes, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= d\\d &= q\\q &= p\\5n + 10d + 25q + 1p &= 164\end{align*}
b A LaTex expression showing \begin{align*}p &= n\\n &= d\\d &= q\\1p + 5n + 10d + 25q &= 164\end{align*}
8
An svg image showing a math problem
Some coins have a total value of $1.75 There are the same number of Pennies and Dimes, and the same number of Nickels and Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= d\\n &= q\\1p + 10d + 5n + 25q &= 175\end{align*}
b A LaTex expression showing \begin{align*}p &= n\\q &= d\\1p + 5n + 25q + 10d &= 175\end{align*}