Answer: 25 eggs were broken
Step-by-step explanation:
This is found by applying number theory principles to find the smallest number that leaves a remainder of one when divided by 2, 3, and 4, and is divisible by 5. (This is the easier version of explaining, I made it so you don't have to write too much.)
The student is asking about a number theory problem involving finding a number that leaves a remainder of one when divided by 2, 3, and 4, and no remainder when divided by 5. This problem requires finding the least common multiple (LCM) of the divisors and then considering the additional constraints given by the remainders.
Firstly, let’s find the LCM of 2, 3, and 4, which is 12. Now, any number that fulfills these conditions must be in the form 12n + 1, where n is a whole number. Since the number also needs to be divisible by 5 without remainders, we look for an instance of 12n + 1 that is also a multiple of 5.
By testing successive multiples of 12 (13, 25, 37, 49, ...), we find that 25 is the first number that meets all conditions: 25 % 2 = 1, 25 % 3 = 1, 25 % 4 = 1, and 25 % 5 = 0. Therefore, Alan had 25 eggs before he broke them.
(Please brainliest if possible, and I hope this brings your grades up, Sorry, if I was wrong!)
