At a concert, 2/7 of the audience were men and 2/5 of the remaining audience were women.The rest were children.
a) what fraction of the audience were children?
b) If there were 42 children, how many people were in the audience?
xcrxrey it did nit fxdr
Let's solve the problem step by step:
a) To find the fraction of the audience that were children, we need to find the fraction of the audience that were neither men nor women.
First, let's find the fraction of the audience that were women:
Since 2/7 of the audience were men, this means 1 - 2/7 = 5/7 of the audience were not men.
Next, let's find the fraction of the remaining audience that were women:
Since 2/5 of the remaining audience were women, this means the fraction of women in the audience is (5/7) * (2/5) = 10/35 = 2/7.
Therefore, the fraction of the audience that were children is (1-2/7-2/7) = (7/7 - 4/7) = 3/7.
So, a) the fraction of the audience that were children is 3/7.
b) If we know that there were 42 children, we can find the total number of people in the audience.
Since the fraction of the audience that were children is 3/7, we can set up the following equation: (3/7) * Total number of people = 42.
To solve for the total number of people, we multiply both sides of the equation by the reciprocal of 3/7, which is 7/3:
(3/7) * Total number of people * (7/3) = 42 * (7/3).
Simplifying, we get:
Total number of people = (42 * 7 * 3) / (3 * 7) = 42.
Therefore, b) the total number of people in the audience is 42.
To find the fraction of the audience that were children, we first need to find the fraction of the audience that were women. Let's break down the problem step by step.
a) Fraction of the audience that were men:
Since 2/7 of the audience were men, this means that 5/7 of the audience were not men.
Fraction of the remaining audience that were women:
Out of the remaining 5/7 of the audience, 2/5 were women. So the fraction of the audience that were women is (2/5) * (5/7).
To find the fraction of the audience that were children:
Since the rest of the audience that were neither men nor women were children, we need to subtract the fraction of men and women from 1.
Fraction of the audience that were children:
1 - (Fraction of men + Fraction of women)
b) To find the total number of people in the audience, we need to set up an equation using the given information:
Let's assume the total number of people in the audience is 'x'.
Fraction of men in the audience = 2/7
Fraction of women in the audience = 2/5 * (5/7) = 2/7
Fraction of children in the audience = 1 - (2/7 + 2/7) = 1 - 4/7 = 3/7
The fraction of children is equal to the number of children divided by the total number of people in the audience, which is 42:
(3/7) * x = 42
Now you can solve for 'x' by multiplying both sides of the equation by 7/3:
x = (42 * 7) / 3 = 98
Therefore, there were 98 people in the audience.
Suppose we had x people in the audience
If 2/7x were men, then 5/7x of the group were non-men
women = (2/5)(5/7x) = 2/7x of the group were women
but 2/7x + 2/7x = 4/7x <--- men and women
which means there were 3/7x children
fraction of audience which were children
= (3/7x) / x
= 3/7
b)
If (3/7)x = 42
x = 42(7/3) = 98
check:
(2/7) of 98 were men ---> 28
leaving 70 women and children
(2/5)(70) were women ----> 28 women
children = 70-28 = 42
second check:
what is (3/7) of 98 ?