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?
Philip can represent how he should sort the acorns by dividing the total number of acorns, 92, by the common number, let's call it x.
Since each group should have an equal number of acorns with tops and without tops, Philip needs to find a number x that satisfies the following conditions:
1) The number of acorns with tops, 66, should be divisible by x without a remainder.
2) The number of acorns without tops, 26, should also be divisible by x without a remainder.
Thus, the correct representation would be to find all numbers that satisfy both conditions. Therefore, the answer options can be:
A) All factors of 92 that are greater than 1.
B) All common factors of 66 and 26.
C) All common multiples of 66 and 26.
D) All prime numbers greater than 1.
The correct answer is option B) All common factors of 66 and 26.
To represent how Philip should sort the acorns, we need to find a common factor between the number of acorns with tops (66) and the number without tops (26). This common factor will determine the number of groups Philip can create with an equal number of acorns with and without tops.
The common factor of 66 and 26 is 2.
To find the number of groups, divide the total number of acorns by the common factor:
92 / 2 = 46
So, Philip can sort the acorns into 46 groups, each with an equal number of acorns with tops (66/2 = 33) and an equal number without tops (26/2 = 13).
what the hell are you guys talking about just what's the answer
To solve this problem, we need to find a way to divide the 92 acorns into groups with the same number of acorns, considering both acorns with tops and acorns without tops.
First, we can determine the highest common factor (HCF) of the two numbers: 66 (acorns with tops) and 26 (acorns without tops). The HCF represents the largest number that divides both 66 and 26 without leaving a remainder.
To find the HCF, we can use the Euclidean algorithm, which involves repeatedly dividing the larger number by the remainder until the remainder becomes zero. The last non-zero remainder is the HCF. Let's find the HCF of 66 and 26:
66 ÷ 26 = 2 remainder 14
26 ÷ 14 = 1 remainder 12
14 ÷ 12 = 1 remainder 2
12 ÷ 2 = 6
Therefore, the HCF of 66 and 26 is 2.
The HCF tells us that we can divide the acorns into groups of 2, where each group has the same number of acorns with tops and without tops. To represent how Philip should sort the acorns, you can write it as follows:
Group 1: 2 acorns with tops, 2 acorns without tops
Group 2: 2 acorns with tops, 2 acorns without tops
...
Group 33: 2 acorns with tops, 2 acorns without tops
Each of the 33 groups would have 2 acorns with tops and 2 acorns without tops, resulting in a balanced sorting of the 92 acorns Philip collected.