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)
1(66+26)
The correct answer is: 6(11+4)
The correct answer is 2(33+13).
To figure out the answer, we need to find a common factor between the number of acorns with tops (66) and the number of acorns without tops (26). A common factor of 66 and 26 is 13. This means that if Philip wants to sort the acorns into groups with the same number of acorns with tops and without tops, each group should have 13 acorns with tops and 13 acorns without tops.
Now, we need to determine how many groups we can create. We have a total of 92 acorns, so we divide this by the number in each group (13+13) to get the number of groups: 92 / (13+13) = 92 / 26 = 3.
Therefore, Philip can sort the acorns into 3 groups, with each group containing 13 acorns with tops and 13 acorns without tops. This can be represented as 2(33+13), where 2 represents the number of groups and 33+13 represents the number of acorns with tops and without tops in each group.