Final answer:
Caroline could only have 10, 11, or 12 quarters combined with 3 dimes to meet the conditions of at least $2.85 in value without exceeding a total of 15 coins, which means 'None of these' is the correct answer.
Step-by-step explanation:
Caroline has 3 dimes and a combination of coins that amount to at least $2.85. A dime is worth $0.10, and a quarter is worth $0.25. Since she has 3 dimes, the value of these dimes is $0.30. We need to subtract this amount from the total amount of $2.85 to find out how much value the quarters need to contribute.
$2.85 - $0.30 gives us $2.55 needed in quarters to reach the minimum total of $2.85. Since each quarter is worth $0.25, we can now divide $2.55 by $0.25 to find the number of quarters:
$2.55 ÷ $0.25 = 10.2 quarters
Since Caroline cannot have a fraction of a quarter, we round down to the nearest whole number which is 10 quarters. However, we need to consider that Caroline can have a maximum of 15 coins, so we need to check all possible values from 10 quarters downwards that still satisfy the conditions of the problem. The possible number of quarters she can have are: 10, 11, or 12. These are the only values that would give a combined total of at least $2.85 and not exceed the maximum number of 15 coins when added to the 3 dimes Caroline already has.
Therefore, the correct combination of quarters that Caroline could have while meeting the given conditions are 10, 11, or 12 quarters. The original answer options provided do not include the correct set of values, so the correct answer is None of these.