I'm having alot of problems with the problem. I don't want the answer but I need to know how to figure it out to get the answer. To put it in another way I don't know where to start.
A farmer takes to market in her cart, but she hit a pothole, which knock over all the containers of eggs. though herself is unhurt, every egg is broken. She goed to her insurance agent, who askes her how many eggs she had. She says she doesn't know, but she remember somthings for various way she tried packing the eggs. She know that when she put the eggs in groups of 2,3,4,5 and 6 she had one left over. when she put the eggs in groups of 7 there were no eggs left over.
Your task is to answer the insurance agent question. What can the farmer figure out from the information about how many eggs that she had? Is there more than one possibility?
You need to find a multiple of 7 that all of the numbers can go into with only 1 left over. I kept multiplying 7 by other numbers until I found the answer. Hint: it's a three-digit number that ends in 1.
To solve this problem, let's break down the information provided:
1. When the farmer put the eggs in groups of 2, 3, 4, 5, and 6, she had one left over.
2. When the eggs were put in groups of 7, there were no eggs left over.
From this information, we can conclude that the total number of eggs must be a multiple of 7.
To determine the possible number of eggs, we can start by finding the least common multiple (LCM) of 2, 3, 4, 5, and 6 (since these group sizes leave one egg leftover). The LCM of these numbers is 60. Therefore, there must be 60 eggs or any multiple of 60 (e.g., 120, 180, etc.).
But since we also know that when the eggs were put in groups of 7, there were no eggs left over, we need to find the multiples of 60 that are also divisible by 7. By dividing different multiples of 60 by 7 and checking for remainders, we find that 420 is the smallest multiple that meets this condition. Therefore, the farmer must have had 420 eggs.
In conclusion, based on the given information, the farmer can figure out that she had 420 eggs. There might be other possibilities for the number of eggs, as the problem does not specify the maximum number of eggs the farmer could have had.