This math topic focuses on formulating algebraic equations based on the number and type of coins that sum up to a specific total value. The problems involve identifying relationships between different coin types (pennies, nickels, dimes, and quarters) and setting up equations that indicate these relationships along with their combined values. The objective is to solve for the unknown number of each coin type using basic algebraic concepts, solidifying skills in creating and solving equations from word problems.

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

more
View

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

Mobius Math Academy logo
Algebra with Coins - Same Count of Two with Three Coin Types - to Equations
1
An svg image showing a math problem
Some coins have a total value of $0.90 There are the same number of Nickels and Dimes but a different number of Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= d\\25q + 5n + 10d &= 90\end{align*}
b A LaTex expression showing \begin{align*}d &= q\\5n + 10d + 25q &= 90\end{align*}
2
An svg image showing a math problem
Some coins have a total value of $0.70 There are the same number of Pennies and Nickels but a different number of Dimes. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\1p + 5n + 10d &= 70\end{align*}
b A LaTex expression showing \begin{align*}p &= d\\1p + 10d + 5n &= 70\end{align*}
3
An svg image showing a math problem
Some coins have a total value of $0.93 There are the same number of Pennies, Nickels, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= p\\p &= n\\25q + 1p + 5n &= 93\end{align*}
b A LaTex expression showing \begin{align*}p &= n\\n &= q\\1p + 5n + 25q &= 93\end{align*}
4
An svg image showing a math problem
Some coins have a total value of $1.23 There are the same number of Nickels and Quarters but a different number of Pennies. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= q\\5n + 25q + 1p &= 123\end{align*}
b A LaTex expression showing \begin{align*}q &= p\\25q + 1p + 5n &= 123\end{align*}
5
An svg image showing a math problem
Some coins have a total value of $1.45 There are the same number of Nickels and Dimes but a different number of Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}n &= q\\10d + 5n + 25q &= 145\end{align*}
b A LaTex expression showing \begin{align*}n &= d\\25q + 5n + 10d &= 145\end{align*}
6
An svg image showing a math problem
Some coins have a total value of $0.83 There are the same number of Pennies and Dimes but a different number of Quarters. What equations would help us solve?
a A LaTex expression showing \begin{align*}d &= p\\10d + 1p + 25q &= 83\end{align*}
b A LaTex expression showing \begin{align*}p &= d\\1p + 10d + 25q &= 83\end{align*}
7
An svg image showing a math problem
Some coins have a total value of $1.24 There are the same number of Pennies, Nickels, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\n &= q\\1p + 5n + 25q &= 124\end{align*}
b A LaTex expression showing \begin{align*}p &= q\\q &= n\\1p + 25q + 5n &= 124\end{align*}
8
An svg image showing a math problem
Some coins have a total value of $0.46 There are the same number of Pennies and Quarters but a different number of Nickels. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= n\\25q + 1p + 5n &= 46\end{align*}
b A LaTex expression showing \begin{align*}p &= q\\5n + 1p + 25q &= 46\end{align*}