A group of girls share a packet of sweets among them. If each girl gets 6 sweets, there will be 4 sweets short. If each girl gets 5 sweets, there will be 3 sweets left over. How many sweets are there in a packet?

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Anonymous Anonymous

03-08-2015
Mathematics

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A group of girls share a packet of sweets among them. If each girl gets 6 sweets, there will be 4 sweets short. If each girl gets 5 sweets, there will be 3 sweets left over. How many sweets are there in a packet?

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JaySL JaySL · Answer 1 · 2015-08-03T21:34:55-04:00

We say that there are \(x\) girls. We equate the two expressions for the amount of sweets in the packet to get:
\(6x-4=5x+3\)
Subtracting 5x from both sides and adding 4 to both sides, we see that:
\(x=7\)
Since there are 7 girls, we have 76-4=38 sweets, using the first expression of the amount of sweets. To check our answer, we examine the second expression for the amount of sweets, for a result of 75+3=38 sweets. Since both of these amounts are equal, our answer seems to be correct. Thus, there are 38 sweets in a packet.