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Linear equations word problem (too many or too few) :1次方程式の文章題(過不足)

Question:  Some pieces of of candy are given to some children. When each child gets 5 pieces of candy, there are 2 pieces too many. When each child gets 6 pieces of candy, there are 4 pieces too few. Find an answer to the number of children and the number of candy pieces in this case. 

How to solve: Assuming that the number of children is x, the number of candy pieces can be expressed in two ways. One is from "When each child gets 5 pieces of candy, there are 3 pieces too many," (5x plus 2) pieces. Another is, from "When each child gets 6 pieces of candy, there are 5 pieces too few," (6x minus 4) pieces. 

 Because these two equations express the same number of candy pieces, it becomes 5x plus 2 equals 6x minus 4. Therefore the number of children is 6. The number of candy pieces is 33. 

 

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