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In the certain party, there was a bowl of rice for every two guests , a bowl of juice for every three of them and a bowl of meat for every four of them. If there were all 65 bowls of food , then how many guests were there in the party ?
- a)65
- b)24
- c)60
- d)48
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In the certain party, there was a bowl of rice for every two guests , ...
Let the number of rice bowls be a, the number of juice bowls be b, and the number of meat bowls be c.
According to question,
a + b + c = 65........................(1)
The total number of guests = 2a
The total number of guests = 3b
The total number of guests = 4c
So the total number of guests will be same in the party.
2a = 3b = 4c..........................(2)
As per Equation (2)
b = 2a/3................................(3)
c = 2a/4 = a/2......................(4)
Now put the value of b and c from Equation (3), (4) in Equation (1),
a + 2a/3 + a/2 = 65
(6a + 4a + 3a)/6 = 65
13a = 65 x 6
a = 5 x 6 = 30
Put the value of a in equation (3) and (4) in order to get the value of b and c,
b = 2 x 30/3 = 2 x 10 = 20
c = 30/2 = 15
The Total number of Guests = 2a = 3b = 4c = 60
According to question,
a + b + c = 65........................(1)
The total number of guests = 2a
The total number of guests = 3b
The total number of guests = 4c
So the total number of guests will be same in the party.
2a = 3b = 4c..........................(2)
As per Equation (2)
b = 2a/3................................(3)
c = 2a/4 = a/2......................(4)
Now put the value of b and c from Equation (3), (4) in Equation (1),
a + 2a/3 + a/2 = 65
(6a + 4a + 3a)/6 = 65
13a = 65 x 6
a = 5 x 6 = 30
Put the value of a in equation (3) and (4) in order to get the value of b and c,
b = 2 x 30/3 = 2 x 10 = 20
c = 30/2 = 15
The Total number of Guests = 2a = 3b = 4c = 60
Most Upvoted Answer
In the certain party, there was a bowl of rice for every two guests , ...
Given Information:
- There is a bowl of rice for every two guests.
- There is a bowl of juice for every three guests.
- There is a bowl of meat for every four guests.
- There are a total of 65 bowls of food.
Let's Solve the Problem:
Step 1: Calculation of Total Bowls
- Let the number of guests be x.
- The total number of bowls of food can be calculated as follows:
- Number of rice bowls = x/2
- Number of juice bowls = x/3
- Number of meat bowls = x/4
- Total number of bowls = x/2 + x/3 + x/4 = 65
Step 2: Finding the Value of x
- To find the value of x, we can solve the equation:
- x/2 + x/3 + x/4 = 65
- Multiplying the equation by 12 to get rid of fractions:
- 6x + 4x + 3x = 780
- 13x = 780
- x = 60
Therefore, the number of guests in the party is 60.
So, option c) 60 is the correct answer.
- There is a bowl of rice for every two guests.
- There is a bowl of juice for every three guests.
- There is a bowl of meat for every four guests.
- There are a total of 65 bowls of food.
Let's Solve the Problem:
Step 1: Calculation of Total Bowls
- Let the number of guests be x.
- The total number of bowls of food can be calculated as follows:
- Number of rice bowls = x/2
- Number of juice bowls = x/3
- Number of meat bowls = x/4
- Total number of bowls = x/2 + x/3 + x/4 = 65
Step 2: Finding the Value of x
- To find the value of x, we can solve the equation:
- x/2 + x/3 + x/4 = 65
- Multiplying the equation by 12 to get rid of fractions:
- 6x + 4x + 3x = 780
- 13x = 780
- x = 60
Therefore, the number of guests in the party is 60.
So, option c) 60 is the correct answer.
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