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37 votes
37 votes
Mrs Chua has a bag of sweets for some children. If each child gets 8 sweets, there will be 3 sweets extra. If she gives each child 9 sweets, there will be 2 sweets short. Find the extra number if sweets Mrs Chua needs to buy in order for each child to get either 8 or 9 sweets​

User Pravin Vavadiya
by
2.9k points

1 Answer

12 votes
12 votes

Answer:

38

Explanation:

It is clear that the number of sweets that should be bought so that each child can get either 8 or 9 sweets should be divisible by both 8 and 9

This is called the LCM or least common multiple of 8 and 9
Since 8 and 9 have no divisors in common LCM of 8 and 9 is 72 so 72 is the minimum number of sweets to buy so that there are no leftovers if each child gets 8 or 9 sweets

Let's compute the number of sweets that were bought the first time. Let the number of children be X

Since each child got 8 sweets and 2 were left over, the total of sweets must be 8X + 2

If each child were to get 9 sweets each then there would be 2 sweets short

This can be written as 9X -2 for the total number of sweets

Since these have to be equal,
9X - 2 = 8X + 2

Add 2 to both sides:
9X - 2 + 2 = 8X +2 + 2
9X = 8X + 4

Subtract 8X from both sides
9X - 8X = 8X - 8X + 4
1X = 4
==> X = 4
So number of children is 4

Total number of sweets bought
= 8 x 4 + 2 = 34

or

= 9 x 4 - 2 = 34

Therefore number of extra sweets to be bought = 72 - 34 = 38

Hope that helps and if you don't understand and need more explanation, please post a comment

User Lionel Tay
by
3.4k points
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