This math topic focuses on creating and solving algebraic equations using coin values, where the amounts and types of coins are specified. Each problem deals with scenarios where there are equal quantities of three different coin types. Students must formulate equations that represent the total monetary value of the coins. This involves understanding the value of different coins (pennies, nickels, dimes, quarters) and applying elementary algebra to find the number of each coin type that sums up to the given total amount. This set of problems is an introductory exercise in algebraic thinking, specifically applying equations to practical situations.

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

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Algebra with Coins - Same Count of Three with Three Coin Types - to E...
1
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Some coins have a total value of $1.44 There are the same number of Pennies, Dimes, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}p &= d\\d &= q\\1p + 10d + 25q &= 144\end{align*}
b A LaTex expression showing \begin{align*}d &= p\\p &= q\\10d + 1p + 25q &= 144\end{align*}
2
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Some coins have a total value of $2.00 There are the same number of Nickels, Dimes, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= n\\n &= d\\25q + 5n + 10d &= 200\end{align*}
b A LaTex expression showing \begin{align*}n &= d\\d &= q\\5n + 10d + 25q &= 200\end{align*}
3
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Some coins have a total value of $0.80 There are the same number of 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\\5n + 10d + 25q &= 80\end{align*}
b A LaTex expression showing \begin{align*}d &= q\\q &= n\\10d + 25q + 5n &= 80\end{align*}
4
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Some coins have a total value of $0.40 There are the same number of 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\\5n + 10d + 25q &= 40\end{align*}
b A LaTex expression showing \begin{align*}q &= d\\d &= n\\25q + 10d + 5n &= 40\end{align*}
5
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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 &= n\\n &= p\\25q + 5n + 1p &= 93\end{align*}
b A LaTex expression showing \begin{align*}p &= n\\n &= q\\1p + 5n + 25q &= 93\end{align*}
6
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Some coins have a total value of $1.20 There are the same number of 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\\5n + 10d + 25q &= 120\end{align*}
b A LaTex expression showing \begin{align*}q &= d\\d &= n\\25q + 10d + 5n &= 120\end{align*}
7
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Some coins have a total value of $1.55 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 &= 155\end{align*}
b A LaTex expression showing \begin{align*}p &= n\\n &= q\\1p + 5n + 25q &= 155\end{align*}
8
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Some coins have a total value of $0.80 There are the same number of Nickels, Dimes, and Quarters, and only those coins. What equations would help us solve?
a A LaTex expression showing \begin{align*}q &= d\\d &= n\\25q + 10d + 5n &= 80\end{align*}
b A LaTex expression showing \begin{align*}n &= d\\d &= q\\5n + 10d + 25q &= 80\end{align*}