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Question 1142693: At a school function, 4/9 of the audience was female and the rest were male. 1/3 of the adults are female. If there were 85 male children, how many persons altogether attend the program.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of males in attendance.
let y = the number of females in attendance.
x + y = number of people in attendance.
4/9 * (x + y) = number of females.
5/9 * (x + y) = number of males.
you are given that 1/3 of the adults are females.
this means that 2/3 of the adults have to be male.
if 2/3 of the adults have to be male, then the number of adult males is equal to 2/3 * 5/9 * (x + y).
this means that the number of male children has to be equal to 1/3 * 5/9 * (x + y).
since the number of male children is equal to 85, you get:
1/3 * 5/9 * (x + y) = 85
solve for x + y to get x + y = 85 * 3 * 9/5 = 459.
this implies that the number of people in attendance was 459.
that should be your solution.
working through the numbers with the assumption that the total number of attendees is 459, i get the following.
4/9 * 459 = 204 females in attendance.
5/9 * 459 = 255 males in attendance.
of the males in attendance, 85 are children.
that makes 170 adult males in attendance.
if 1/3 of the adults in attendance are female, then 2/3 of the adults in attendance have to be male.
let z = number of adults, then you get 2/3 * z = 170.
that makes z = 170 * 3/2 = 255.
this means that 255 of the attendees are adults.
170 of them are male.
85 of them are female.
1/3 * 255 = 85 (females).
2/3 * 255 = 170 (males).
if 85 females are adult, then 204 - 85 = 119 females in attendance are children.
if you work up a chart, it would look like this.
male female total
adults 170 85 255
children 85 119 204
total 255 204 459
ratio of males to total is 255 / 459 = 5/9
ratio of females to total is 204 / 459 = 4/9
ratio of female adults to total adults is 85 / 255 = 1/3.
ratio of male adults to total adults is 170 / 255 = 2/3.
i'm pretty sure your solution is that the total number of people in attendance is equal to 459.
Answer by ikleyn(52805)  (Show Source):
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