Philip is sorting acorns he collected. He has 92 acorns: 66 still have their tops, 26 do not. Philip wants to sort the acorns into groups with the same number of acorns, including some with and without tops. He wants each group to have an equal number of acorns with tops and an equal number of acorns without tops. Which answer best shows how Philip can represent how he should sort the acorns?(1 point)

Question

Responses

2(33+13)
2 left parenthesis 33 plus 13 right parenthesis

1(66+26)
1 left parenthesis 66 plus 26 right parenthesis

6(11+4)
6 left parenthesis 11 plus 4 right parenthesis

24(3+1)
24 left parenthesis 3 plus 1 right parenthesis

Answer 1

To find a way for Philip to sort his acorns so that each group has an equal number of acorns with tops and without tops, we should first look at the total counts.

Philip has:

• 66 acorns with tops
• 26 acorns without tops

This gives us a total of 92 acorns.

To sort them into equal groups, we need to factor both the number of acorns with tops (66) and the number without tops (26) to find a common divisor.

Let's check the number of groups he can form:

For 66 acorns (with tops): The factors are: 1, 2, 3, 6, 11, 22, 33, 66

For 26 acorns (without tops): The factors are: 1, 2, 13, 26

The common factors of 66 and 26 include 1 and 2. Hence, the maximum number of groups Philip can create, where he has equal parts of both types in his groups, is with the common factor 2.

If he sorts them into 2 groups:

• Each group will have \( \frac{66}{2} = 33 \) acorns with tops
• Each group will have \( \frac{26}{2} = 13 \) acorns without tops

Thus, he can represent how he should sort the acorns as: \[ 2(33 + 13) \]

Among the provided options, the correct answer is: 2(33 + 13).