Question

Suppose there is a pile of​ quarters, dimes, and pennies with a total value of ​$1.18. ​(a). How much of each coin can be present without being able to make change for a​ dollar? If there are multiple selections of coins that will​ work, choose the selection with the largest total number of coins. ​(b). Explain why​ $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar.

Answer 1

To determine the number of quarters, dimes, and pennies without being able to make change for a dollar, we find the maximum number of each coin. The largest total number of coins is 4 quarters, 5 dimes, and 53 pennies. $1.19 is the greatest amount of money without making change for a dollar because of the available coin denominations.

Step-by-step explanation:

To determine how many quarters, dimes, and pennies can be present without being able to make change for a dollar, we need to find the highest possible number of each coin that still results in a total value of $1.18. Let's start by considering the quarters. Since each quarter is worth 25 cents, the maximum number of quarters that can be present without making change for a dollar would be 4, as 4 * 25 cents = 100 cents = $1. Now, let's find the maximum number of dimes. Each dime is worth 10 cents, so with 4 quarters already accounted for, we have 50 cents left. The maximum number of dimes that can be present without making change for a dollar would be 5, as 5 * 10 cents = 50 cents. Finally, we need to find the maximum number of pennies. With 4 quarters and 5 dimes already accounted for, we have 53 cents left. Since each penny is worth 1 cent, the maximum number of pennies that can be present without making change for a dollar would be 53. Therefore, the selection with the largest total number of coins would be 4 quarters, 5 dimes, and 53 pennies.

Now, let's move on to part (b). To explain why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar, we need to consider the available coin denominations. The highest denomination is the quarter, which is worth 25 cents. If we have 4 quarters, the remaining amount we can't make change for is $1 - $1 = $0. With 5 dimes, each worth 10 cents, the remaining amount we can't make change for is $0.10. And with 99 pennies, each worth 1 cent, the remaining amount we can't make change for is $0.01. Therefore, the greatest amount of money it is possible to have without being able to make change for a dollar is $1.19.

Answer 2

A) 3 quarters, 4 dimes 3 pennies = 0.75 +0.40 +0.03 = 1.18

B) 3 * .25 + 4 * .10 + 4* .01 = x

.75 + .40 + .04 = x

1.19 = x

If you have 4 quarters, you have change for 1 dollar.

If you have 5 dimes, you have change for 2 quarters.

If you have any nickels, 1 of those could combine with 2 dimes to have change for a quarter.

If you have 5 pennies, you have enough change for 1 nickel.