The answer is (E).When 120 candies are given to 25 children and the number of candies for each child is at most 7, what is the maximum number of children who get only 1 candy?
Méthode 1
-> substitue choices to find max number. Since 9 is the biggest number, it would be better start from (E).
-> If each of 9 children get only 1 candy, 9 candies were distributed, and 111 candies and 16 children remained.
-> Can we distribute 111 candies to 16 children within the terms we were given? - yes.
-> We can give 7 candies to 15 children and 6 candies to remaining one children. (\(15\frac{6}{7}\))
-> Therefore 9 is the max number of children who get only 1 candy.
Methode 2
-> visualization
-> There is 25 children {??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??|??}
-> First, let’s distribute 1 candy to each child. {?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?|?}
-> We are left with 95 candies now.
-> Since we want to know max number of children who get 1 candy, let’s allow some kids to have max number of candies they can get.
Because if you distribute another round of 1 candy per kid equally, there wouldn’t be a kid with only one candy.
-> Since everyone has at least one candy in their hand, we can give out 6 candies per kid, and \(\frac{95}{6}=15\frac{5}{6}\)
{
[?|?|?|?|?|?|?|?|?|?|?|?|?|?|?]|
?|?|?|?|?|?|?|?|?|?}
-> Highlighted candies are children who got 7 candies in total, and underlined candy is a child who got 6 candies in total.
-> Therefore, 9 children left with only one candy in thier hand.
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