Problem number 21. A box has fewer than 50 cookies in it. The cookies can be divided evenly between 2, 3, or 4 children. However, they cannot be divided evenly between 7 children because 6 more cookies would be needed. How many cookies are there in the box? A-12, B-24, C-30, D-36, or E-48. First, we're going to find numbers that are less than 50 that are divisible by 2, 3, and 4. After we do so, we're going to see which of these numbers could be divided by 7 if we added 6 to it. The number of cookies has to be divisible by 2, 3, and 4. Any number that's divisible by 4 is divisible by 2. However, if a number is divisible by 4 and by 3, that means it's divisible by 12 because the least common multiple of 3 and 4 is 12. So the multiples of 12 are 12, 24, 36, 48, and any other ones would be more than 50. So these are the ones we're going to work with. Now let's add 6 to each of these numbers and see which of these numbers is divisible by 7. 12 plus 6 is 18. 18 is not divisible by 7, so this is not our number. 24 plus 6 is 30. 30 is not divisible by 7, so that's not the number. 36 plus 6 is 42. 42 is divisible by 7 because 7 times 6 is 42. And 48 plus 6 is 54. 54 is not divisible by 7. So of the numbers that we found that are multiples of 12 that are less than 50, only 36 becomes a multiple of 7 when we add 6 to it. So the number we're looking for is 36, and there are 36 cookies in the box.

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