Matthew had 740 stickers and he was able to give them away equally among his classmates. His class had between 30 to 40 pupils. How many more stickers would Matthew need if he wanted to give each classmate 25 stickers instead?

- ISMC (International Singapore Maths Competition) Grade 5

Solution:

To be able to divide 740 stickers among 30-40 classmates equally, 740 should be perfectly divisible by the total number of classmates. Hence the number of classmates should be a factor of 740.

Let's list the factors of 740. You need to look for a factor of 740 that is in between 30 and 40. You do not need to find out all the factors. I've just listed them for explanation.

Factors of 740: 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740

So the only factor of 740 that is between 30 and 40 is 37.

Hence there should be 37 students in the class.

Now the rest of the problem becomes simple. If there are 37 students and each classmate gets 25 stickers, then Matthew needs 37*25=925 stickers. Which means he needs 925-740=185 more stickers.

Hence Matthew needs 185 more stickers.

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