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**Hint:**In the given question, we have been asked to find the number of ways in which we can make one dollar with using pennies and dimes only. Pennies and dimes are the most common coins. They are each worth to the different amount of money i.e. 1 penny is worth 1 cent and 1 dime is worth 10 cents.

**Complete step by step solution:**

The value of penny and dime is as follows:

1 penny = 1 cent

1 dime = 10 cents

To make one dollar either we can use 100 pennies or we can use 10 dimes, as

1 dollar = 100 cents, and

10 dime = \[10\times 10\ cents=100\ cents\]

100 pennies = \[1\times 100=100\ cents\]

Different ways to make one dollar with pennies and dimes only:

1) 10 dimes and 0 pennies

10 dimes = \[10\times 10\ cents=100\ cents\]= 1 dollar

2) 9 dimes and 10 pennies

9 dimes = \[9\times 10\]= 90 cents

10 pennies = \[1\times 10\]= 10 cents

Together,

9 dimes and 10 cents = 90 cents + 10 cents = 100 cents = 1 dollar

3) 8 dimes and 20 pennies

8 dimes = \[8\times 10\]= 80 cents

20 pennies = 20 cents

Together,

8 dimes and 20 pennies = 80 cents + 20 cents = 100 cents = 1 dollar

4) 7 dimes and 30 pennies

7 dimes = \[7\times 10\]= 70 cents

30 pennies = 30 cents

Together,

7 dimes and 30 pennies = 70 cents +38 dimes and 20 pennies

5) 6 dimes and 40 pennies

6 dimes = \[6\times 10\]= 60 cents

40 pennies = 40 cents

Together,

6 dimes and 40 pennies = 60 cents + 40 cents = 100 cents = 1 dollar

6) 5 dimes and 50 pennies

5 dimes = \[5\times 10\]= 50 cents

50 pennies = 50 cents

Together,

5 dimes and 50 pennies = 50 cents + 50 cents = 100 cents = 1 dollar

7) 4 dimes and 60 pennies

4 dimes = \[4\times 10\]= 40 cents

60 pennies = 60 cents

Together,

4 dimes and 60 pennies = 40 cents + 60 cents = 100 cents = 1 dollar

8) 3 dimes and 70 pennies

3 dimes = \[3\times 10\]= 30 cents

70 pennies = 70 cents

Together,

3 dimes and 70 pennies = 30 cents + 70 cents = 100 cents = 1 dollar

9) 2 dimes and 80 pennies

2 dimes = \[2\times 10\]= 20 cents

80 pennies = 80 cents

Together,

2 dimes and 80 pennies = 20 cents + 80 cents = 100 cents = 1 dollar

10) 1 dimes and 90 pennies

1 dimes = \[1\times 10\]= 10 cents

90 pennies = 90 cents

Together,

1 dimes and 90 pennies = 10 cents + 90 cents = 100 cents = 1 dollar

11) 0 dimes and 100 pennies

100 pennies = 100 cents = 1 dollar

**Therefore, there are 11 ways in which we can make one dollar with only using pennies and dimes.**

**Note:**

To answer this question, students first should be very well-known with the terms of penny and dime. As it may have seen that most of the time students don't understand what pennies and dimes are. Later the students should remember the worth of each coin and the worth of dollar in the same measure, so then they will be able to solve this question very easily.

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