Mr baker baked some muffins. If he packs them in boxes of 4, he will have 3 left over. If he packs them in boxes of 5 he will also have 3 left over. If he packs them in boxes of 6 he will have only 1 left over find the least possible number of muffins mr Baker baked
So you are looking for a number which
1. when divided by 4 leaves a remainder of 3
2. when divided by 5 leaves a remainder of 3
3. when divided by 6 leaves a remainder of 1
Since we are dealing with relatively small numbers we can just list the sequences of numbers for each case:
1: 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63 67 71
2: 8 13 18 23 28 33 38 43 48 53 58 63 68 73
3: 7 13 19 25 31 37 43 49 55 61 67 73 79
well ....
To solve this problem, we need to find the least possible number of muffins that satisfy all of the given conditions.
Let's start by setting up the equations:
1) If Mr. Baker packs the muffins in boxes of 4, he will have 3 left over. This can be represented by the equation:
Number of muffins ≡ 3 (mod 4)
2) If Mr. Baker packs the muffins in boxes of 5, he will have 3 left over. This can be represented by the equation:
Number of muffins ≡ 3 (mod 5)
3) If Mr. Baker packs the muffins in boxes of 6, he will have 1 left over. This can be represented by the equation:
Number of muffins ≡ 1 (mod 6)
To find the least possible number of muffins, we can find the least common multiple (LCM) of 4, 5, and 6 and then add the respective remainders.
The LCM of 4, 5, and 6 is 60. Let's consider multiples of 60 and add the remainders:
1) 3 (mod 4): The first multiple of 60 that leaves a remainder of 3 when divided by 4 is 3 itself.
2) 3 (mod 5): The first multiple of 60 that leaves a remainder of 3 when divided by 5 is 63.
3) 1 (mod 6): The first multiple of 60 that leaves a remainder of 1 when divided by 6 is 61.
To find the least possible number of muffins, we need to find the maximum among these three cases: 63.
Therefore, the least possible number of muffins Mr. Baker baked is 63.