# Puzzle | Marriage Party

3 types of people go to a marriage party.

Type 1 people : 1 man eats in 4 plates.

Type 2 people : 1 man eats in 2 plates.

Type 3 people : 4 men eat in 1 plate.

You are given that exactly 100 people go to the party and there are exactly 100 plates. So you have to calculate how many people of type 1, type 2 and type 3 will go to the party. Whereby the condition is all the 100 plates should be consumed by 100 people. And no plate will remaining after the party.

Solution :

Let no. of plates consumed by people of type 1 are x, type 2 are y, and type 3 are z.

=> **x + y + z = 100 ….(1)**

So no. of plates consumed by type 1 are 4x, type 2 are 2y, and type 3 are z.

=> **x/4 + y/2 + 4z = 100 ….(2)**

( x will be the multiple of 4 and y will be the multiple of 2 because the no. of plates will be an Integer value)

By solving these two equations we get :-

=>** 14z – x = 200 ….(3)**

Now you have to manually find all value of x, and z from eq.(3) by considering their conditions

**Conditions :**

1) 15 < = z <= 24 (because eq.(3)) minimum no. of z will be 15 because if we take 14 then eq(3) will not satisfied, and maximum no. of z will be 24 because if we take 24 plates then 96 people and if take 25 plates then 100 people which is not possible because type 1 and type 2 are also exist there and z belongs to I.

2) 1 <= x <= 97 and will be the multiple of 4, x belongs to I.

3) 1 <= y <= 95 and will be the multiple of 2, y belongs to I.

And put the value of x, z in eq(1) and find y. If condition satisfied then it will be our final result.

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