1. Shalvi wants to organize her birthday party. She is very health conscious, thus shedecided to serve fruits only. She has 36 apples and 60 bananas at home and decided toserve them. She want to distribute fruits among guests. She does not want todiscriminate among guests so she decided to distribute equally among all.(i) How many maximum guests Shalvi can invite?(ii) How many apples and bananas will each guest get?(iii) Shalvi decide to add 42 mangoes also. In this case how many maximum guestsShalvi caninvite ?(iv) How many total fruits will each guest get?(v) If Shalvi decide to add 3 more mangoes and instead 6 apple, in this case howmany maximum guests Shalvi can invite ?
Question
- Shalvi wants to organize her birthday party. She is very health conscious, thus shedecided to serve fruits only. She has 36 apples and 60 bananas at home and decided toserve them. She want to distribute fruits among guests. She does not want todiscriminate among guests so she decided to distribute equally among all.(i) How many maximum guests Shalvi can invite?(ii) How many apples and bananas will each guest get?(iii) Shalvi decide to add 42 mangoes also. In this case how many maximum guestsShalvi caninvite ?(iv) How many total fruits will each guest get?(v) If Shalvi decide to add 3 more mangoes and instead 6 apple, in this case howmany maximum guests Shalvi can invite ?
Solution
(i) To determine the maximum number of guests Shalvi can invite, we need to find the greatest common divisor (GCD) of the number of apples and bananas she has. The GCD of 36 and 60 is 12. Therefore, Shalvi can invite a maximum of 12 guests.
(ii) Since Shalvi wants to distribute the fruits equally among all the guests, each guest will receive an equal number of apples and bananas. To find out how many apples and bananas each guest will get, we divide the total number of apples and bananas by the number of guests. In this case, each guest will receive 36/12 = 3 apples and 60/12 = 5 bananas.
(iii) If Shalvi decides to add 42 mangoes to the existing fruits, we need to consider the GCD of the total number of fruits (apples, bananas, and mangoes) to determine the maximum number of guests she can invite. The GCD of 36, 60, and 42 is 6. Therefore, Shalvi can invite a maximum of 6 guests.
(iv) To find out how many total fruits each guest will get, we divide the total number of fruits (apples, bananas, and mangoes) by the number of guests. In this case, each guest will receive (36 + 60 + 42)/6 = 24 fruits.
(v) If Shalvi decides to add 3 more mangoes and instead of 6 apples, we need to recalculate the maximum number of guests she can invite. The GCD of 39, 54, and 42 is 3. Therefore, Shalvi can invite a maximum of 3 guests.
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