Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?
Answer (2)
The question requires finding the smallest number of coins Freddie needs to make any amount of money up to one dollar using pennies, nickels, dimes, and quarters. Since a dollar equals 100 pennies, and smaller units are required to make up larger units, the goal here is to have enough coins to make any combination of cents up to 99 since 100 cents would already be a dollar.
Starting with pennies, we need at least one penny to be able to pay any amount that includes an odd number of cents. For example, we would need a penny to make a payment of one cent.
Next, nickels are needed to pay any amount ending in 5 when greater than 5 cents and less than a dime. To cover every five-cent increment up to 95 cents, we need one nickel.
To account for the tens, we need dimes. A single dime can help create any multiple of ten up to 90 cents in conjunction with quarters which handle the larger denominations. Therefore, we need one dime.
Finally, quarters are necessary to pay multiples of 25 cents. To ensure we can pay any amount from 25 cents to 75 cents, we require three quarters, as four quarters would make a full dollar.
Therefore, we add up our coin needs: one penny, one nickel, one dime, and three quarters, which totals the smallest number of coins Freddie needs: six coins.
Freddie needs a total of 6 coins to pay any amount less than a dollar: 1 penny, 1 nickel, 1 dime, and 3 quarters. This combination allows him to create any cent value from 1 to 99. The chosen coins cover all required increments effectively.
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