answer and solution of lucy had 2 1/2 apples.she cut into fourths. if she had enough fourths for herself and the friends with her, how many of them were there?
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To find the number of friends Lucy had with her, we need to divide the total number of fourths by the number of fourths each person received.
The number of fourths that Lucy had after cutting the 2 1/2 apples into fourths can be calculated as follows:
2 1/2 = 5/2 apples
Since each apple is divided into 4 fourths, the total number of fourths is (5/2) x 4 = 20/2 = 10 fourths.
Let's say each person received 'n' fourths. To find the number of friends, we divide the total number of fourths (10) by 'n' and solve for 'n':
10 / n = number of friends
We need to find a value of 'n' that is an integer and divides 10 evenly.
The possible values of 'n' that divide 10 evenly are 1, 2, 5, and 10.
If 'n' is 1, then 10 / 1 = 10, which means there were 10 friends.
If 'n' is 2, then 10 / 2 = 5, which means there were 5 friends.
If 'n' is 5, then 10 / 5 = 2, which means there were 2 friends.
If 'n' is 10, then 10 / 10 = 1, which means there was 1 friend.
Therefore, Lucy could have had either 10, 5, 2, or 1 friend with her.
To find the answer to this problem, we need to follow the given information step by step.
Let's start with the information that Lucy had 2 1/2 apples. When written as a mixed number, 2 1/2 is equivalent to 5/2.
Next, we are told that she cut the apples into fourths. So, each apple is divided into four equal parts. Since Lucy had 5/2 apples, we need to multiply this by 4 to determine how many fourths she had in total.
5/2 * 4 = 20/2 = 10
Therefore, Lucy had a total of 10 fourths of apples.
We are also told that she had enough fourths for herself and the friends with her. This implies that the total number of fourths should be divisible evenly among Lucy and her friends.
To find how many friends were there, we need to find a factor of 10 (the number of fourths of apples) that represents the number of friends:
Factors of 10: 1, 2, 5, 10
Since Lucy is included in the count, we need to find a factor that is greater than 1. In this case, the factor is 2.
Hence, there were a total of 2 friends with Lucy.
Therefore, the answer to the question "How many of them were there?" is three, including Lucy.