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8.9: Coin Stumpers

Difficulty Level: At Grade Created by: CK-12

Coin Stumpers – Reason Proportionally with Metric Measurements

Teacher Notes

Students reason proportionally about weights of coins in grams. They use those weights to solve multi-step problems. All weights are given to the nearest tenth of a gram.

The Extra for Experts include the values of the coins as an additional factor to consider in the problem solutions.

Solutions:

Coin Stumpers 1

2.3 grams

50 nickels are \begin{align*}50 \times 5\end{align*}50×5 grams, or 250 grams; \begin{align*}273 - 250 = 23\end{align*}273250=23 grams for 10 dimes. One dime is \begin{align*}\frac{23}{10}\end{align*}2310, or 2.3 grams.

Coin Stumpers 2

80 pennies

20 nickels are \begin{align*}20 \times 5\end{align*}20×5 grams or 100 grams. \begin{align*}300 - 100 = 200\end{align*}300100=200 grams.

\begin{align*}\frac{200}{2.5} = 80\end{align*}2002.5=80 pennies.

Coin Stumpers 3

20 pennies and 40 dimes

50 grams is \begin{align*}\frac{50}{2.5}\end{align*}502.5, or 20 pennies. \begin{align*}142 - 50 = 92\end{align*}14250=92 grams.

\begin{align*}\frac{92}{2.3} = 40\end{align*}922.3=40 dimes

Coin Stumpers 4

20 nickels

20 pennies are \begin{align*}20 \times 2.5\end{align*}20×2.5 grams \begin{align*}= 50\end{align*}=50 grams; 18 dimes are \begin{align*}18 \times 2.3\end{align*}18×2.3 grams \begin{align*}= 41.4\end{align*}=41.4 grams. \begin{align*}191.4 - 91.4 = 100\end{align*}191.491.4=100 grams.

\begin{align*}\frac{100}{5} = 20\end{align*}1005=20 nickels.

Coin Stumpers – Reason Proportionally with Metric Measurements

A pile of 100 pennies weighs 250 grams.

A nickel weighs twice as much as a penny.

What is the weight of a pile of 300 coins, half pennies and half nickels?

\begin{align*}& \mathbf{Describe:} && 100 \ \text{pennies weigh} \ 250 \ \text{grams.}\\ &&& \text{A nickel weighs twice as much as a penny.}\\ &&& \text{A new pile has} \ 300 \ \text{coins. Half of the} \ 300 \ \text{are pennies and half are nickels.}\\ \\ & \mathbf{My \ job:} && \text{Figure out the weight of the pile of} \ 300 \ \text{coins, half pennies and half nickels.}\\ \\ & \mathbf{Plan:} && \text{Compute the weight of a penny and a nickel. Then, use those weights to figure out}\\ &&& \text{the weight of the pile of} \ 300 \ \text{coins, half pennies and half nickels.}\\ \\ & \mathbf{Solve:} && 100 \ \text{pennies are} \ 250 \ \text{grams.}\\ &&& \text{So, one penny is} \ \frac{250}{100}, \ \text{or} \ 2.5 \ \text{grams.}\\ &&& \text{One nickel is} \ 2 \times 2.5, \ \text{or} \ 5 \ \text{grams.}\\ &&& 150 \times 2.5 = 375 \ \text{grams}\\ &&& 150 \times 5.0 = 750 \ \text{grams}\\ &&& \text{The pile of} \ 300 \ \text{coins is} \ 1125 \ \text{grams.}\\ \\ & \mathbf{Check:} && 100 \ \text{pennies are} \ 250 \ \text{grams. Using a proportion, the weight of} \ 150 \ \text{pennies is} \ 1.5\\ &&& \text{times} \ 250, \ \text{or} \ 375 \ \text{grams.}\\ &&& \text{Since} \ 100 \ \text{pennies are} \ 250 \ \text{grams}, \ 100 \ \text{nickels are} \ 2 \times 250 \ \text{or} \ 500 \ \text{grams. So}, \ 150\\ &&& \text{nickels are} \ 1.5 \times 500, \ \text{or} \ 750 \ \text{grams.}\\ &&& 375 + 750 = 1125 \ \text{grams}\end{align*}

You have already figured out the numbers of grams for a penny and a nickel. Record the number of grams for a dime once you solve problem 1. Then use those weights to solve the other problems on this page and on the page of Extra for Experts.

Show the steps of your solution to each problem.

\begin{align*}1. \ \quad \text{The weight of a pile of nickels and dimes is} \ 273 \ \text{grams. There are} \ 60 \ \text{coins in the pile. Fifty}\!\\ {\;} \ \ \quad \text{of the coins are nickels. What is the weight of a dime? Record that number in the list above.}\!\\ \\ \\ \\ 2. \ \quad \text{The weight of a pile of pennies and nickels is} \ 300 \ \text{grams. There are} \ 20 \ \text{nickels. How many}\!\\ {\;} \ \ \quad \text{pennies are there?}\!\\ \\ \\ \\ 3. \ \quad \text{The weight of a pile of pennies and dimes is} \ 142 \ \text{grams. The total weight of the pennies is} \ 50 \ \text{grams.}\!\\ {\;} \ \ \quad \text{How many pennies and dimes are in the pile?}\!\\ \\ \\ \\ 4. \ \quad \text{The total weight of a pile of pennies, nickels and dimes is} \ 191.4 \ \text{grams. There are} \ 20 \ \text{pennies}\!\\ {\;} \ \ \quad \text{in the pile. There are} \ 2 \ \text{fewer dimes than pennies. How many coins are nickels?}\!\\ \\ \\ \\ \end{align*}

Extra for Experts: Coin Stumpers – Reason Proportionally with Metric Measurements

Use the coin weights to solve these problems.

Show the steps of your solution to each problem.

\begin{align*}1. \ \quad \text{The total weight of a pile of pennies and dimes is} \ 96 \ \text{grams. There are} \ 20 \ \text{dimes in the pile.}\!\\ {\;} \ \ \quad \text{What is the total value of the coins?}\!\\ \\ \\ \\ 2. \ \quad \text{The total weight of a pile of nickels and pennies is} \ 3000 \ \text{grams. The total value of the nickels}\!\\ {\;} \ \ \quad \text{is} \ \$25. \ \text{How many pennies are in the pile?}\!\\ \\ \\ \\ 3. \ \quad \text{A pile of pennies, nickels and dimes weighs} \ 146 \ \text{grams. There are} \ 30 \ \text{pennies in the pile.}\!\\ {\;} \ \ \quad \text{There are} \ 10 \ \text{less dimes than pennies. What is the total value of the nickels in the pile?}\!\\ \\ \\ \\ 4. \ \quad \text{A pile of pennies, nickels and dimes weighs} \ 195.5 \ \text{grams. There are} \ 15 \ \text{pennies in the pile.}\!\\ {\;} \ \ \quad \text{There are} \ 12 \ \text{more nickels than pennies. What is the total value of the coins in the pile?}\!\\ \\ \\ \\ \end{align*}

Solutions:

Coin Stumpers Extra 1

$2.20

20 dimes is \begin{align*}20 \times 2.3\end{align*} grams, or 46 grams

\begin{align*}96 - 46 = 50\end{align*} grams

\begin{align*}\frac{50}{2.5} = 20\end{align*} pennies

20 dimes is $2.00

20 pennies is $0.20

\begin{align*}\$2 + \$0.20 = \$2.20\end{align*}

Coin Stumpers Extra 2

200 pennies

\begin{align*}\$25 \times 20\end{align*} nickels/dollar \begin{align*}= 500\end{align*} nickels

\begin{align*}500 \times 5\end{align*} grams \begin{align*}= 2500\end{align*} grams of nickels

\begin{align*}3000 - 2500 = 500\end{align*} grams of pennies

\begin{align*}\frac{500}{2.5} = 200\end{align*} pennies

Coin Stumpers Extra 3

$.25

30 pennies is \begin{align*}30 \times 2.5\end{align*}, or 75 grams.

20 dimes is \begin{align*}20 \times 2.3\end{align*}, or 46 grams.

\begin{align*}146 - 75 - 46 = 25\end{align*} grams of nickels

\begin{align*}\frac{25}{5} = 5\end{align*} nickels

5 nickels are $.25

Coin Stumpers Extra 4

$2.50

15 pennies is \begin{align*}15 \times 2.5\end{align*}, or 37.5 grams.

27 nickels is \begin{align*}27 \times 5\end{align*}, or 135 grams.

\begin{align*}195 - 27.5 - 135 = 23\end{align*} grams for dimes.

\begin{align*}\frac{23}{2.3} = 10\end{align*} dimes.

15 pennies are $.15, 27 nickels are $1.35, and 10 dimes are $1.00.

\begin{align*}\$.15 + \$1.35 + \$1.00 = \$2.50\end{align*}

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