Question

I had some pennies, nickels, dimes, and quarters in my pocket. When I reached in and pulled out some change, I had less than 10 coins whose value was 42 cents. What are all the possibilities for the coins I had in my hand?

Answer 1

The student asked about the possible combinations of coins that add up to 42 cents, considering they had less than 10 coins. By breaking down the values of US currency, several combinations are identified such as 1 quarter, 1 dime, 7 pennies, etc., showcasing different ways to reach the total of 42 cents.

Step-by-step explanation:

Possible Combinations of Coins with a Total Value of 42 Cents

To find out all the possibilities for the coins with a total value of 42 cents, we have to consider the denominations of US currency - pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents). Since you mentioned having less than 10 coins, we need to explore combinations that add up to 42 cents without exceeding 9 coins.

Here are the possible combinations:

1 quarter, 1 dime, 7 pennies (9 coins in total)

1 quarter, 2 nickels, 2 pennies (5 coins in total)

1 quarter, 1 nickel, 7 pennies (8 coins in total)

4 dimes, 2 pennies (6 coins in total)

3 dimes, 4 nickels (7 coins in total)

3 dimes, 3 nickels, 2 pennies (8 coins in total)

2 dimes, 6 nickels (8 coins in total)

2 dimes, 5 nickels, 1 penny (8 coins in total)

1 dime, 8 nickels (9 coins in total)

1 dime, 7 nickels, 1 penny (9 coins in total)

0 dimes, 8 nickels, 2 pennies (10 coins, disallowed as it exceeds the amount specified)

These combinations reflect different ways of making up 42 cents with available coins, considering that you cannot have more than 9 coins in total.