cinema hall contains a certain number of people. If 2212% are children, 4712% are men and 84 are women, find the number of men in the hall.
A. 63
B. 84
C. 113
D. 133
Let's assume the total number of people in the cinema hall is x.
Therefore, 2212% of x are children, which is (2212/100)*x = 22.12x.
4712% of x are men, which is (4712/100)*x = 47.12x.
We know that the number of women is 84.
So, the total number of people in the cinema hall can be written as:
22.12x + 47.12x + 84 = x
Simplifying the equation, we get:
69.24x + 84 = x
68.24x = 84
x = 84/68.24
x ≈ 1.231
Since x is not a whole number, we need to find the number of men rounded to the nearest whole number.
Therefore, the number of men in the cinema hall is approximately 47 men (because 47.12 multiplied by 1.231 is approximately 57.85).
Therefore, the answer is option B. 84.
To find the number of men in the cinema hall, we can start by calculating the percentage of the total number of people that are men. We know that 4712% are men, which means that 4712 out of every 100 are men.
To calculate the actual number of men, we need to find what 4712% is equal to. We can do this by setting up the following equation:
4712/100 = x/total
Where x is the unknown total number of people in the cinema hall.
Now we know that the number of women is 84. So, we can write another equation:
84 = (100 - 4712)/100 * total
Simplifying this equation, we get:
84 = (100 - 47.12) * total / 100
84 = 52.88 * total / 100
To solve for the total number of people, we can multiply both sides of the equation by 100 and divide by 52.88:
84 * 100 / 52.88 = total
Simplifying, we get:
159.36 ≈ total
Since we can't have fractional people, we'll round this number to the nearest whole number:
total ≈ 159
Now we know the total number of people in the cinema hall is approximately 159.
To find the number of men, we can calculate:
4712/100 * 159 = 7.5128 ≈ 8 men
Therefore, the number of men in the cinema hall is approximately 8.
Since none of the options given match the calculated value, there may be an error in the provided information or calculations. Please review the information and calculations used to find the number of men in the hall.