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Sir i am confused with this problem. Pls help. Thanks

Julie has fewer than 50 sweets If she packs the sweets into group of 5, she will have 3 sweets left. if she packs the sweets into group of 6, she will have 13 sweets left. how many sweets does she have?

Hello, Angel.

We know that Julie has fewer than 50 sweets. The most she can have, therefore, is 49.

If she packs the sweets into groups of 5, she will have 3 left, but simultaneously, if she packs them into groups of 6, she will have 13 left. This doesn't really make sense since that group of 13 sweets can be made into two more groups of 6, plus one more sweet.

Regardless, we can still proceed. I advise first asking what numbers are divisible by 6. 6, 12, 18, 24, 30, 36, 42, and 48 are all divisible by 6, and yet less than 50. 42 and 48 are out because though these are divisible by 6, there won't be 13 remaining afterwards.

36 is divisible by 6, and it's possible to have a surplus of 13 (giving you a total of 49), but 49 cannot be arranged in groups of 5 with a remainder of 3. (5 x 9 = 45, but this would yield a remainder of 4.)

30 does work. You can make 5 groups of 6 (6 x 5 = 30), and with a surplus of 13 sweets, this gives Julie a grand total of 43. 43 sweets can also be organized into 8 groups of 5, with a remainder of 3.

6, 12, 18, and 24 do not work for the same reason that 36 doesn't.

The answer is 43 sweets.

Hope this helps.

Regards,

John

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