Final answer:
To make 27 cents using an odd number of quarters, dimes, nickels, and pennies, there are three ways. These include using one quarter with two pennies, three nickels with twelve pennies, or one nickel with twenty-two pennies.
Step-by-step explanation:
The original question asks for the number of ways to make 27 cents using quarters, dimes, nickels, and pennies, specifically using an odd number of coins. Since a quarter is worth 25 cents and is the largest coin of the four, we can only use one quarter or none because two would exceed 27 cents. After using a quarter, we're left with 2 cents, which can be made with two pennies – an odd number of coins in total (1 quarter + 2 pennies = 3 coins).
If we don't use a quarter, we need to consider combinations of dimes, nickels, and pennies to make 27 cents with an odd number of coins.
- Two dimes and seven pennies (total 9 coins).
- One dime, three nickels, and two pennies (total 6 coins, which is even and not considered).
- One dime, one nickel, and twelve pennies (total 14 coins, which is even and not considered).
- Three nickels and twelve pennies (total 15 coins).
- One nickel and twenty-two pennies (total 23 coins).
Therefore the total number of ways to make 27 cents with an odd number of coins is three ways: using a quarter and two pennies, three nickels and twelve pennies, or one nickel and twenty-two pennies.