There are less than 27 dozen eggs in a large basket. If you count them 3, 5, 7 or 9 at a time, there are none left over. How many eggs are in the basket?
Answers
Answer:
Solution:
This problem asks us to find a number that is less than 72 and a multiple of 3, but also satisfies the other given criteria.
Using a list of multiples of 3 less than 72 would be a good method to solving this problem.
Multiples of 3
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
Now let’s eliminate some of these multiples.
We know there are less than 72 eggs and there must be at least 6. We also know that the number of eggs can’t be even because when counted by two there is one egg remaining. So that leaves us with the following:
Multiples of 3
9
15
21
27
33
39
45
51
57
63
69
Because there’s a remainder when the eggs are counted by 5, we can also eliminate the multiples of five.
Multiples of 3
9
21
27
33
39
51
57
63
69
Of the remaining multiples of 3, lets find the number that leaves a remainder of 3, when divided by 4, 5, and 6. (There’s only one!)
Multiples of 3
63
The only number that satisfies all of the given criteria is 63. Therefore, there are 63 eggs in the basket!