Solve the problem.
Bruce has 98¢. What combination of coins could he not have?
Select the correct answer.
Question 1 options:
1 quarter, 7 dimes, 3 pennies
3 quarters, 2 dimes, 2 pennies
3 quarters, 2 dimes, 3 pennies
Question 2 (2 points)
The correct answer is 3 quarters, 2 dimes, 3 pennies.
To solve this problem, we need to determine the combination of coins that would result in a total of 98¢. Then, we can identify which of the given options does not match the calculated combination.
Let's analyze the options:
Option 1: 1 quarter, 7 dimes, 3 pennies
(1 quarter) x (25¢) + (7 dimes) x (10¢) + (3 pennies) x (1¢) = 25¢ + 70¢ + 3¢ = 98¢
Option 2: 3 quarters, 2 dimes, 2 pennies
(3 quarters) x (25¢) + (2 dimes) x (10¢) + (2 pennies) x (1¢) = 75¢ + 20¢ + 2¢ = 97¢
Option 3: 3 quarters, 2 dimes, 3 pennies
(3 quarters) x (25¢) + (2 dimes) x (10¢) + (3 pennies) x (1¢) = 75¢ + 20¢ + 3¢ = 98¢
From the analysis above, we can conclude that the combination Bruce could not have is:
Option 2: 3 quarters, 2 dimes, 2 pennies
Therefore, the correct answer is Option 2.
To solve this problem, we need to determine the total value of each combination of coins and then compare it to the given amount of 98¢ to see which combination is not possible.
In this case, we have three options:
1. 1 quarter, 7 dimes, 3 pennies:
The value of 1 quarter is 25¢, 7 dimes is 70¢, and 3 pennies is 3¢. Adding them together, we get 25¢ + 70¢ + 3¢ = 98¢. Therefore, this combination is possible.
2. 3 quarters, 2 dimes, 2 pennies:
The value of 3 quarters is 75¢, 2 dimes is 20¢, and 2 pennies is 2¢. Adding them together, we get 75¢ + 20¢ + 2¢ = 97¢. Therefore, this combination is not possible as it is 1¢ short of the given amount.
3. 3 quarters, 2 dimes, 3 pennies:
The value of 3 quarters is 75¢, 2 dimes is 20¢, and 3 pennies is 3¢. Adding them together, we get 75¢ + 20¢ + 3¢ = 98¢. Therefore, this combination is possible.
Based on this analysis, the combination that Bruce could not have is:
3 quarters, 2 dimes, 2 pennies.
So, the correct answer is:
3 quarters, 2 dimes, 2 pennies.