Coin Problems

1
Coin Problems

• Students will use Guess and Check Chart and
  Algebra to solve Coin Word Problems

2
What are coins worth?

• A penny
• A nickel
• A dime
• A quarter

.01 .05 .10 .25
What are 5 pennies worth? What are 7 nickels
worth? What are 8 dimes worth? What are 9
quarters worth?
5(.01) .05 7(.05) .35 8(.10) .80 9(.25)
2.25
3
Setting Up A Guess Check Chart

• Set up a column for each coin in problem
• The last column should be for Total Amount of
  Money

4

• Bill has four times as many quarters as dimes.
  He has 2.20 altogether. How many of each coin
  does he have?

Total (2.20)
Q (4D)
D (?)
Key Phrase Four times as many quarters as dimes
This tells us that if we know how many dimes We
can figure out how many quarters So our guess
column will be the Dime column
5

• Bill has four times as many quarters as dimes.
  He has 2.20 altogether. How many of each coin
  does he have?

The guess column
Total (2.20)
Q (4D)
D (?)
5(.10) 20(.25) .50 5.00 5.50
20
5
6

• Bill has four times as many quarters as dimes.
  He has 2.20 altogether. How many of each coin
  does he have?

Total (2.20)
Q (4D)
D (?)
5(.10) 20(.25) .50 5.00 5.50
20
5
3(.10) 12(.25) .30 3.00 3.30
12
3
2(.10) 8(.25) .20 2.00 2.20
8
2
We found the total!!!
Bill has 2 dimes and 8 quarters
7

• Bill has four times as many quarters as dimes.
  He has 2.20 altogether. How many of each coin
  does he have?

To convert to Algebraic Equation
The guess column becomes x!
Total (2.20)
Q (4D)
D (?)
2(.10) 8(.25) .20 2.00 2.20
8
2
X(.10) 4x(.25) 2.20
4x
X
The Total Column becomes the equation!
8
Using Algebra to Solve

• STEPS
• Define variables
• Write an equation
• Solve equation
• Answer question !

9

• Bill has four times as many quarters as dimes.
  He has 2.20 altogether. How many of each coin
  does he have?

The guess column becomes x!
D (?) Q (4D) Total (2.20)
X 4x x(.10) 4x(.25) 2.20
The Total Column becomes the equation!
x(.10) 4x(.25) 2.20 .10x 1.00x 2.20 1.10x
2.20 x 2
Answer Bill has 2 dimes and 8 quarters.
Let x dimes Let 4x quarters
Hint Keep 2 decimal places so your numbers look
like money
10
Paul has twice as many dimes as pennies and 3
times as many nickels as pennies. He has 1.80.
How many of each type of coin?

• Set up chart !!!

If we know how many pennies, we can figure
nickels dimes!
Start Guessing!
Total (1.80)
D (2P)
N (3P)
P (?)
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Paul has twice as many dimes as pennies and 3
times as many nickels as pennies. He has 1.80.
How many of each type of coin?
Total (1.80)
D (2P)
N (3P)
P (?)
2(.01) 6(.05) 4(.10) .02.30.40.72
4
6
2
4(.01) 12(.05)8(.10) .04.60.801.44
8
12
4
5(.01) 15(.05) 10(.10) .05.751.001.80
10
15
5
Paul had 5 pennies, 15 nickels, and 10 dimes.
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Paul has twice as many dimes as pennies and 3
times as many nickels as pennies. He has 1.80.
How many of each type of coin?
Total (1.80)
D (2P)
N (3P)
P (?)
5(.01) 15(.05) 10(.10) .05.751.001.80
10
15
5
X(.01)3x(.05)2x(.10)1.80
2x
3x
X
X(.01)3x(.05)2x(.10) 1.80 .01x.15x.20x1.80
.36x1.80 X5
Let x pennies Let 3xnickels Let 2xdimes
Paul had 5 pennies, 15 nickels and 10 dimes.
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Wrapping It Up-Coin Problems

• How do you label your Guess Check chart?
• How do you decide which column is x?
• What is the most important thing you will do when
  solving a word problem?

• All coins and Total Amount
• The guess column
• Answer the question!!!!!!