# Fun with mathematics

## This is the last of a four-part series of maths questions presented by Marshall Cavendish Education. The questions are targeted at pupils in upper primary, and the worked solutions and advice have been contributed by Associate Professor Lee Ngan Hoe, Assistant Head (Mathematics Education - Teaching) of the Mathematics & Mathematics Education Academic Group from the National Institute of Education at Nanyang Technological University. Prof Lee is also the co-author of Shaping Maths and Maths Works!

QUESTION 4

Ken buys some mangoes. If he packs them equally into bags of 40, he will have seven mangoes left. If he packs them equally into five bags, he will need to buy more mangoes. What is the smallest number of mangoes he needs to buy?

SOLUTION TO QUESTION 4

If the mangoes are packed equally into bags of 40, the total number of mangoes in all the bags must be a multiple of 40.

Since 40 = 4 x 10, the total number of mangoes in all the bags must be a multiple of 10. In other words, the digit in the ones place for the total number of mangoes in all the bags must be 0.

We also know that if Ken packs the mangoes equally into bags of 40, he will have seven mangoes left. Thus, the digit in the ones place for the total number of mangoes Ken has is seven.

For Ken to pack his mangoes equally into five bags, the number of mangoes he eventually has must be a multiple of five.

So the digit in the ones place must be 0 or 5.

Since the digit in the ones place for the number of mangoes Ken now has is 7, the smallest number of mangoes he needs to buy is three, to make the digit in the ones place a 0 or 5.

• Try to understand the problem first. What is the problem about? What information is given to you and how does it help you to better make sense of the problem? What does it mean to say that if Ken packs the mangoes "equally into bags of 40, he will have seven mangoes left"? What else do you know based on this information? What does it mean to say that Ken "packs them equally into five bags"? What else do you know about the new number of mangoes Ken has? What are you supposed to find? What is meant by the "smallest number" of mangoes he needs to buy?

• Work out a plan to solve the problem. Do you have enough information to know the number of mangoes that Ken originally had? If not, what do you think this number may look like? Is there a pattern that all the possible numbers must follow? How about the final number of mangoes Ken has? Can you tell what this number may look like?

•Try to make sense of the answer. Is there a way to check it? What have you learnt from solving this problem? Can you create a similar problem for others to solve? This would help you better understand such problems and develop more effective strategies to handle them.