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Chapter 7: Problem 386

How many different sums of money can be obtained by choosing two coins from a box containing a penny, a nickel, a dime, a quarter, and a half dollar?

Short Answer

Expert verified
There are 10 different sums of money that can be obtained by choosing two coins from the box containing a penny, a nickel, a dime, a quarter, and a half dollar.

Step by step solution

01

List the coin values

First, we write down the values of each coin in cents. We will use these values to find the different possible sum values. - Penny: 1 cent - Nickel: 5 cents - Dime: 10 cents - Quarter: 25 cents - Half Dollar: 50 cents
02

Find all unique pairs of coins

Now let's find all unique combinations of picking two coins from the box. We need to make sure we don't consider the same pair of coins twice. We can do this by listing all possible pairs in a systematic way: (Penny, Nickel), (Penny, Dime), (Penny, Quarter), (Penny, Half Dollar), (Nickel, Dime), (Nickel, Quarter), (Nickel, Half Dollar), (Dime, Quarter), (Dime, Half Dollar), (Quarter, Half Dollar) There are 10 unique pairs of coins.
03

Calculate the sum values for each pair

Now we will calculate the sum values for each unique pair of coins that we found in step 2: 1. Penny (1 cent) + Nickel (5 cents): 6 cents 2. Penny (1 cent) + Dime (10 cents): 11 cents 3. Penny (1 cent) + Quarter (25 cents): 26 cents 4. Penny (1 cent) + Half Dollar (50 cents): 51 cents 5. Nickel (5 cents) + Dime (10 cents): 15 cents 6. Nickel (5 cents) + Quarter (25 cents): 30 cents 7. Nickel (5 cents) + Half Dollar (50 cents): 55 cents 8. Dime (10 cents) + Quarter (25 cents): 35 cents 9. Dime (10 cents) + Half Dollar (50 cents): 60 cents 10. Quarter (25 cents) + Half Dollar (50 cents): 75 cents We can see that each sum is unique.
04

Count the number of different sum values

Now we count the number of unique sum values we found in step 3. There are 10 unique sums, which corresponds to the number of unique pairs of coins. So, the number of different sums of money that can be obtained by choosing two coins from the box is 10.

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