Philip is sorting acorns he collected. He has 92 acorns: 66 still have there tops, 26 do not. Philip wants to sort the acorns into groups with the same number of acorns 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 and an equal number without tops. Which answer best shows how philip can represent how he can sort the acorns.
A possible way for Philip to represent how he can sort the acorns is by using a table with two columns.
On the left column, he can write "Acorns with Tops" and label the rows with numbers representing the different possible numbers of acorns with tops in each group (e.g. 0, 2, 4, 6, etc.).
On the right column, he can write "Acorns without Tops" and label the rows with numbers representing the different possible numbers of acorns without tops in each group (e.g. 0, 2, 4, 6, etc.).
He can then fill out the table by finding pairs of numbers that add up to 92 (the total number of acorns) and placing one number in the left column and the other number in the right column.
For example, he can have one row with "Acorns with Tops" = 26 and "Acorns without Tops" = 66, as this represents a group with 26 acorns without tops and 66 acorns with tops.
He can continue to fill out the table with different combinations until he has sorted all the acorns.
To sort the acorns in the desired way, Philip can divide them into groups based on the common factors of the total number of acorns with and without tops.
Let's start by finding the factors of the number of acorns with tops, which is 66:
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Now, let's find the factors of the number of acorns without tops, which is 26:
Factors of 26: 1, 2, 13, 26
To have equal numbers of acorns with and without tops in each group, Philip needs to find common factors of 66 and 26. The common factors are 1 and 2.
Therefore, Philip can represent how he can sort the acorns into groups as follows:
Group 1: 2 acorns with tops, 2 acorns without tops (Factor: 2)
Group 2: 1 acorn with tops, 1 acorn without tops (Factor: 1)
Note: This is just one possible representation, and there may be other ways to sort the acorns with equal numbers of acorns with tops and without tops in each group.
To find the answer to this question, let's break down the information provided and analyze the options given.
We know that Philip has 92 acorns in total. Out of these, 66 still have their tops, and 26 do not. Philip wants to sort the acorns into groups where each group has an equal number of acorns with tops and an equal number without tops.
Let's examine the answer choices:
A) 2 groups of 29 acorns each, with 22 acorns with tops and 7 without tops.
B) 4 groups of 23 acorns each, with 16 acorns with tops and 7 without tops.
C) 4 groups of 29 acorns each, with 22 acorns with tops and 7 without tops.
D) 2 groups of 46 acorns each, with 33 acorns with tops and 13 without tops.
To represent how Philip can sort the acorns, we need to find an option where both the number of acorns with tops and without tops are divided equally among the groups.
In option A, there are 22 acorns with tops and 7 without tops. However, dividing them into two groups of 29 acorns each would not result in an equal distribution of both types.
Option B divides the acorns equally into four groups of 23 acorns each. However, there are 16 acorns with tops and only 7 without tops, making it an unequal distribution.
Option C divides the acorns into four groups of 29 acorns each, with 22 acorns with tops and 7 without tops. This aligns with Philip's requirement of equal distribution of both types, so it seems like a reasonable answer.
Option D suggests dividing the acorns into two groups of 46 acorns each, with 33 acorns with tops and 13 without tops. While this maintains an equal number of each type within the groups, it does not divide the acorns into multiple smaller groups as mentioned in the question.
Based on the analysis, the best answer that represents how Philip can sort the acorns according to the given conditions is:
C) 4 groups of 29 acorns each, with 22 acorns with tops and 7 without tops.