Question

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?

Answer 1

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 7*6-4=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 7*5+3=38 sweets.  Since both of these amounts are equal, our answer seems to be correct.  Thus, there are 38 sweets in a packet.