Question 1207595: Hi
At a carnival the ratio of females to males was 7 to 10 . The ratio of men to boys was 5 to 4. The ratio of women to girls was 5 to 4.
What fraction were children.
If there were 450 more men than women how many males were at the carnival.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
The ratio of females to males was 7 to 10:
Let 7x = # of females
Let 10x = # of males
The ratio of men to boys was 5 to 4:
Let 5y = # of men
Let 4y = # of boys
The number of males is equal to the number of men plus the number of boys:
5y+4y = 10x
To avoid having to work with ugly fractions, "scale up" the definitions of the numbers of men and boys so that the sum is a multiple of 10:
Let 50y = # of men
Let 40y = # of boys
Now the number of males is 50y+40y = 90y.
The number of males is 90y; and the number of females is 7/10 of the number of males. So the number of females is 7/10 of 90y, which is 63y.
The ratio of women to girls was 5 to 4:
Let 5z = # of women
Let 4z = # of girls
The number of females (63) is the sum of the numbers of women and girls:
5z+4z=63y
9z=63y
z=7y
The number of women was 5z=35y; the number of girls was 4z=28y.
We now have....
# of men = 50y
# of boys = 40y
# of women = 35y
# of girls = 28y
First question -- what fraction of the people were children?
# of children = 40y+28y = 68y
# of people = 50y+40y+35y+28y=153y
fraction of the people that were children: 68y/153y = 68/153 = 4/9
ANSWER: 4/9 of the people were children
Second question -- If there were 450 more men than women how many males were at the carnival?
The number of men was 450 more than the number of women:
50y-35y=450
15y=450
y=30
# of males = 90y = 90*30 = 2700
ANSWER: There were 2700 males at the carnival
Answer by ikleyn(52887)  (Show Source):
You can put this solution on YOUR website! .
Hi
At a carnival the ratio of females to males was 7 to 10 . The ratio of men to boys was 5 to 4.
The ratio of women to girls was 5 to 4. What fraction were children.
If there were 450 more men than women how many males were at the carnival.
~~~~~~~~~~~~~~~~~~~~~~~~~
The formulation of this problem is accessible to young students, who know fractions,
but are not familiar with equations. Therefore, it is natural to expect that the solution
is accessible for such students. Below I produce such a solution.
The ratio of men to boys was 5 to 4. It is the same as to say that the ratio of boys to men was 4 to 5.
The ratio of women to girls was 5 to 4. It is the same as to say that the ratio of girls to women was 4 to 5.
At this point, we see that it would be ideally, if you could count men by groups of 5,
as well as to count women by groups of 5.
The ratio of women to men was 7 to 10 (given). 7:10 is the same as 14:20, the same as 21:30,
the same as 28:40 and the same as 35:50.
As soon as you see this pair, 35 and 50, you understand that in this case you can count the men and the women by groups of 5.
So, if there are 35 men and 50 women, it implies that there are 28 boys and 40 girls.
Now the ratio under the problem question is
boys + girls 28 + 40 68
fraction of children = ---------------- = ----------- = ------.
men + women 35 + 50 85
Divide the numerator and denominator by 17 (the common factor and the greatest common divisor)
and get the answer: the fraction of children is 4:5.
Solved.
This solution does not require using any equations.
It only requires elementary skills of manipulating fractions.
|
|
|
