Question 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) Responses 24(3+1) 24 left parenthesis 3 plus 1 right parenthesis 2(33+13) 2 left parenthesis 33 plus 13 right parenthesis 6(11+4) 6 left parenthesis 11 plus 4 right parenthesis 1(66+26)

Answer 1

To find how Philip can sort the acorns into groups with an equal number of acorns with and without tops, we need to find a common divisor for both the number of acorns with tops (66) and the number of acorns without tops (26).

The greatest common divisor (GCD) of 66 and 26 is 2. This means Philip can create groups of acorns in pairs, where each group has the same ratio of acorns with tops and acorns without tops.

If he creates groups of size 2, then:

• For the acorns with tops: 66 acorns / 2 = 33 groups of acorns with tops.
• For the acorns without tops: 26 acorns / 2 = 13 groups of acorns without tops.

Thus, each group will consist of 1 acorn with a top and 1 acorn without a top.

Here, the option that correctly represents this sorting method is:

2(33 + 13)

This represents 2 groups of 33 acorns with tops and 13 acorns without tops in total.

So the correct response is: 2(33 + 13).