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In detail

The celebration

The celebration

All the students in my class went to celebrate the end of the course at a restaurant. To save money, we ordered a total of 65 dishes so that the salad plates are shared between every 4, pizza dishes between every 3 and desserts between every 2.

How many students are in my class?

Solution

Since we have to divide the students into groups of 4, 3 and 2, we will try a multiple of them all. The smallest multiple with which we can try is 12. In the case that there were 12 students in the restaurant, they would need 3 salad plates, 4 pizzas and 6 desserts, which would make a total of 13 dishes.

As we know that the amount of dishes that were really ordered were 65, which is 5 times more (65 = 13 × 5), that indicates that the number of students was 5 times 12, that is, 12 × 5 = 60 which are all the students in my class.