At a dinner party, every 3 guests used a dish for rice between them; every 4 a dish for broth; every 2 a dish for meat. There were 65 dishes in all. How many guests were there?
Let the number of guests be x
then
x/3 + x/4 + x/2 = 65
Multiply bye 12 to get
4x + 3x + 6x = 780
I get x = 60
check:
rice dishes = 60/3 = 20
broth = 60/4 = 15
meat = 60/2 = 30
20+15+30 = 65 check!!
Let's work through the problem step by step to find the number of guests at the dinner party.
First, let's assume there were "x" guests at the dinner party.
According to the problem, every 3 guests used a dish for rice, every 4 guests used a dish for broth, and every 2 guests used a dish for meat.
To find the number of dishes used for rice, we divide the total number of guests (x) by 3. This gives us x/3 dishes for rice.
To find the number of dishes used for broth, we divide the total number of guests (x) by 4. This gives us x/4 dishes for broth.
To find the number of dishes used for meat, we divide the total number of guests (x) by 2. This gives us x/2 dishes for meat.
The sum of the dishes used for rice, broth, and meat should equal the total number of dishes, which is 65 according to the problem.
So, we can set up an equation: x/3 + x/4 + x/2 = 65.
To solve this equation, we will find a common denominator for the fractions on the left side, which is 12.
(x*4 + x*3 + x*6)/12 = 65.
Simplifying the equation, we have: (4x + 3x + 6x)/12 = 65.
Combining like terms, we have: 13x/12 = 65.
To isolate x, we multiply both sides of the equation by 12: 13x = 65 * 12.
Dividing both sides of the equation by 13, we find: x = (65 * 12) / 13.
Evaluating the expression on the right side of the equation, we find: x = 780 / 13.
Therefore, there were 60 guests at the dinner party.