A dinner party

Algebra Level 2

At a dinner party every 2 guests used a dish of rice between them.Every three guests used a dish of dhal and every four used a dish of meat between them.there were altogether 65 dishes.How many guests were present?


The answer is 60.

Priyam Gupta by Priyam Gupta , 27, India

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4 solutions

Anzar Aznzar
Mar 29, 2014

65 = (x/2) + (x/3) + (x/4)

65 = (6x+4x+3x) /12

13x/12=65

x=(65*12)/13 = 780/13 = 60

1 Helpful 0 Interesting 0 Brilliant 0 Confused

got the same solution..

Louella Mamuyac - 7 years, 2 months ago
Ace Octavo
Mar 29, 2014

6+3+4/12*60

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kunal Mahanwar
Mar 23, 2014

LCM of 2,3 &4 is 12 so they will require 13 dishes and 65 dishes are present so 12*65/13=60

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Harshal Sheth
Feb 16, 2014

Each person uses 1 2 + 1 3 + 1 4 \frac{1}{2}+\frac{1}{3}+\frac{1}{4} dishes, or 13 12 \frac{13}{12} dishes. It follows that there were 60 \boxed{60} guests at the party.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Let the number of bowls of rice = x Let the number of bowls of veggies = y Let the number of bowls of meat = z Let the number of guests = g

x + y + z = 65 2x = 3y = 4z = g

2x = 3y y = 2/3 x

2x = 4z z = x/2

x + 2/3x + x/2 = 65 x + 7/6 x = 65 13x/6 = 65 x = 30

g = 2*30 g = 60

There are 60 guests.

Aditya Dutta - 7 years, 3 months ago

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