A dinner party was attended by 1000 people 800 people had Pasta 720 pe...
Given information:
- Total number of guests at the dinner party = 1000
- Number of guests who had Pasta = 800
- Number of guests who had Burgers = 720
- Number of guests who had Pizza = 750
- 64% of the total guests had all three items
- All those except 80 guests who had Pizza also had Burgers
- All those except 60 guests who had Burgers also had Pasta
- 85% of the total guests who had Pasta also had Pizza
Calculating the number of guests who had all three items:
Let's assume the number of guests who had all three items as x.
According to the given information, 64% of the total guests had all three items, so we can write the equation:
0.64 * 1000 = x
Solving the equation, we find:
0.64 * 1000 = x
x = 640
Therefore, there were 640 guests who had all three items (Pasta, Burgers, and Pizza).
Calculating the number of guests who had only Pasta and Pizza:
Let's assume the number of guests who had only Pasta and Pizza as y.
According to the given information, 85% of the total guests who had Pasta also had Pizza, so we can write the equation:
0.85 * 800 = y + 640
Solving the equation, we find:
0.85 * 800 = y + 640
y = 680
Therefore, there were 680 guests who had only Pasta and Pizza.
Calculating the number of guests who had only Burgers and Pizza:
Let's assume the number of guests who had only Burgers and Pizza as z.
According to the given information, all those except 80 guests who had Pizza also had Burgers, so we can write the equation:
750 - 80 = z + 640
Solving the equation, we find:
670 = z + 640
z = 30
Therefore, there were 30 guests who had only Burgers and Pizza.
Calculating the number of guests who had only Pasta and Burgers:
Let's assume the number of guests who had only Pasta and Burgers as w.
According to the given information, all those except 60 guests who had Burgers also had Pasta, so we can write the equation:
720 - 60 = w + 640
Solving the equation, we find:
660 = w + 640
w = 20
Therefore, there were 20 guests who had only Pasta and Burgers.
Calculating the number of guests who had only Pasta:
Let's assume the number of guests who had only Pasta as p.
We know that the total number of guests who had Pasta is 800, and we have already calculated the number of guests who had both Pasta and Pizza (680) and the number of guests who had both Pasta and Burgers (20).
So, we can write the equation:
800 = p + 680 + 20
Solving the equation, we find:
800 = p + 700
p = 100
Therefore, there were 100 guests who had only Pasta.
Calculating the number of guests who had only Burgers:
Let's assume the number of guests who
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