Coin Stumpers
Carol Findell
Mary Cavanagh
Carole Greenes
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Printed: March 15, 2016
AUTHORS
Carol Findell
Mary Cavanagh
Carole Greenes
www.ck12.org
C HAPTER
Chapter 1. Coin Stumpers
1
Coin Stumpers
Students use proportional reasoning to answer questions about coins. Students use problem solving steps to help.
The weight of a pile of pennies and dimes is 142 grams. The total weight of the pennies is 50 grams. How many
pennies and dimes are in the pile? In this concept, we will learn how to reason proportionally to answer questions
about coins.
Guidance
In order to answer the questions about coins like the one above, use the problem solving steps.
• Start by describing what you know from the information given.
• Next, figure out what your job is in this problem. In all of these problems your job will be to answer a question
about the coins.
• Then, make a plan for how you will solve. Think about what other information you know about the weight of
the coins. See if you can figure out the weight and number of each type of coin in the pile.
• Next, solve the problem.
• Finally, check to make sure that your answer works with the original information given.
Example A
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?
Solution:
We can use problem solving steps to help.
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Describe :
100 pennies weigh 250 grams.
A nickel weighs twice as much as a penny.
A new pile has 300 coins. Half of the 300 are pennies and half are nickels.
My job :
Figure out the weight of the pile of 300 coins, half pennies and half nickels.
Plan :
Compute the weight of a penny and a nickel. Then, use those weights to figure out
the weight of the pile of 300 coins, half pennies and half nickels.
Solve :
100 pennies are 250 grams.
250
, or 2.5 grams.
So, one penny is
100
One nickel is 2 × 2.5, or 5 grams.
150 × 2.5 = 375 grams
150 × 5.0 = 750 grams
The pile of 300 coins is 1125 grams.
Check :
100 pennies are 250 grams. Using a proportion, the weight of 150 pennies is 1.5
times 250, or 375 grams.
Since 100 pennies are 250 grams, 100 nickels are 2 × 250 or 500 grams. So, 150
nickels are 1.5 × 500, or 750 grams.
375 + 750 = 1125 grams
We have already figured out the numbers of grams for a penny and a nickel. Next we will find the number of grams
for a dime in Example B. Then we will use those weights to help with all of the other problems in this concept.
Example B
The weight of a pile of nickels and dimes is 273 grams. There are 60 coins in the pile. Fifty of the coins are nickels.
What is the weight of a dime? Record that number in the list below.
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Chapter 1. Coin Stumpers
Solution:
We can use problem solving steps to help.
Describe: 60 coins weigh 273 grams. 50 of the coins are nickels. The rest of the coins are dimes.
My Job: Figure out the weight of a dime and record it in the list.
Plan: I know the weight of a nickel is 5 grams. Figure out the weight of 50 nickels. Subtract that from the weight
of 273 grams to find the weight of 10 dimes. Then, find the weight of one dime.
Solve: One nickel is 5 grams, so 50 nickels is 50 × 5 grams or 250 grams.
Since the pile of 60 coins weighs 273 grams. 273 − 250 = 23 grams is how much the 10 dimes weigh.
23 grams
One dime is
= 2.3 grams.
10
Check: 50 nickels: 5 grams × 50 = 250 grams
10 dimes: 2.3 grams × 10 = 23 grams
250 + 23 = 273
Example C
The weight of a pile of pennies and nickels is 300 grams. There are 20 nickels. How many pennies are there?
Solution:
We can use problem solving steps to help.
Describe: There is a pile of pennies and nickels that weighs 300 grams. There are 20 nickels.
My Job: Figure out how many pennies there are.
Plan: I know that a penny weighs 2.5 grams and a nickel weighs 5 grams. Find the weight of 20 nickels. Subtract
that from 300 grams to find the weight of the pennies. Divide the weight of the pennies by 2.5 grams to find out how
many pennies there are.
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Solve: One nickel weighs 5 grams so 20 nickels weighs 20 × 5 grams = 100 grams.
The pile is 300 grams, so that means that the pennies weigh 300 grams − 100 grams = 200 grams.
200 grams
One penny weighs 2.5 grams. 2.5 grams = 80 so 80 pennies weigh 200 grams. There are 80 pennies in the pile.
Check: 20 nickels: 5 grams × 20 = 100 grams
80 pennies: 2.5 grams × 80 = 200 grams
100 + 200 = 300
Concept Problem Revisited
The weight of a pile of pennies and dimes is 142 grams. The total weight of the pennies is 50 grams. How many
pennies and dimes are in the pile?
We can use the information from the examples and problem solving steps to help us solve this problem.
Describe: There is a pile of pennies and dimes that weighs 142 grams. The pennies weigh 50 grams.
My Job: Figure out how many pennies and dimes are in the pile.
Plan: Use the fact that the whole pile is 142 grams and the pennies are 50 grams to find the weight of the dimes.
I know that a penny weighs 2.5 grams and a dime weighs 2.3 grams. Use this information to find out how many
pennies and dimes there are.
Solve: 142 grams − 50 grams = 92 grams so the dimes weigh 92 grams.
50 grams
2.5 grams = 20 so there are 20 pennies.
92 grams
2.3 grams = 40 so there are 40 dimes.
One penny weighs 2.5 grams.
One dime weighs 2.3 grams.
Check: 20 pennies: 2.5 grams × 20 = 50 grams
40 dimes: 2.3 grams × 40 = 92 grams
50 + 92 = 142
Vocabulary
In this concept we used proportional reasoning when we used what we knew about a pile of coins to figure out
information about one coin. Any time there is a constant ratio between two quantities (such as the number of
pennies in a pile and the weight of the pile) we can use proportional reasoning to solve.
Guided Practice
1. The total weight of a pile of pennies, nickels, and dimes is 191.4 grams. There are 20 pennies in the pile. There
are 2 fewer dimes than pennies. How many coins are nickels?
2. The total weight of a pile of pennies and dimes is 96 grams. There are 20 dimes in the pile. What is the total value
of the coins?
3. The total weight of a pile of nickels and pennies is 3000 grams. The total value of the nickels is $25. How many
pennies are in the pile?
Answers:
1. 20 nickels
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Chapter 1. Coin Stumpers
20 pennies are 20 × 2.5 grams = 50 grams; 18 dimes are 18 × 2.3 grams = 41.4 grams. 191.4 − 91.4 = 100 grams.
100
5 = 20 nickels.
2. $2.20
20 dimes is 20 × 2.3 grams, or 46 grams
96 − 46 = 50 grams
50
2.5 = 20 pennies
20 dimes is $2.00
20 pennies is $0.20
$2 + $0.20 = $2.20
3. 200 pennies
$25 × 20 nickels/dollar = 500 nickels
500 × 5 grams = 2500 grams of nickels
3000 − 2500 = 500 grams of pennies
500
2.5 = 200 pennies
Explore More
1. A pile of pennies, nickels and dimes weighs 146 grams. There are 30 pennies in the pile. There are 10 less
dimes than pennies. What is the total value of the nickels in the pile?
2. A pile of pennies, nickels and dimes weighs 195.5 grams. There are 15 pennies in the pile. There are 12 more
nickels than pennies. What is the total value of the coins in the pile?
3. The total weight of a pile of pennies, nickels, and dimes is 84.6 grams. There are 22 pennies in the pile. There
are 20 fewer dimes than pennies. How many coins are nickels?
4. The total weight of a pile of pennies and nickels is 142.5 grams. There are 15 nickels in the pile. What is the
total value of the coins?
5. The total weight of a pile of nickels and dimes is 1273.1 grams. The total value of the nickels is $10.50. How
many dimes are in the pile?
5