The ratio of the number of males to the females at a performance is 5 : 7.
1/4 of the males and 3/4 of the females are children. What is the ratio of the number of adults to children?
Express your answer in simplest form.
Let's say there are 5x males and 7x females. Now, to divide things up into quarters, let's call that 20y males and 28y females.
That means there are 5y+21y=26y children
So, 26y of the 48y people are children, leaving 22y as adults.
Thus, the adult:children ratio
22:26 = 11:13
To find the ratio of adults to children, we first need to determine the number of males and females separately.
Let's assume that the number of males can be represented by the value x. Then the number of females can be represented by the value y.
According to the given ratio, the number of males to females is 5:7. So we can set up the equation:
x/y = 5/7
Next, we are told that 1/4 of the males are children. This means that 3/4 of the males are adults. Using this information, we can determine the number of male adults and children.
The number of male adults would be 3/4 of the total males:
Male adults = (3/4) * x
And the number of male children would be 1/4 of the total males:
Male children = (1/4) * x
In a similar way, we can find the number of female adults and children.
Now, it's given that 3/4 of the females are children. So the number of female children can be calculated as:
Female children = (3/4) * y
Similarly, the number of female adults would be:
Female adults = (1/4) * y
Now let's simplify the expressions for each group:
Male adults = (3/4) * x
Male children = (1/4) * x
Female adults = (1/4) * y
Female children = (3/4) * y
Now, we can find the total number of adults and children:
Total adults = Male adults + Female adults
Total adults = (3/4) * x + (1/4) * y
Total children = Male children + Female children
Total children = (1/4) * x + (3/4) * y
Finally, we can calculate the ratio of adults to children:
Ratio of adults to children = Total adults / Total children
Ratio of adults to children = [(3/4) * x + (1/4) * y] / [(1/4) * x + (3/4) * y]
To simplify the expression further, we can multiply both the numerator and denominator by 4:
Ratio of adults to children = [(3/4) * x + (1/4) * y] / [(1/4) * x + (3/4) * y]
= [(3x + y) / 4] / [(x + 3y) / 4]
= (3x + y) / (x + 3y)
Therefore, the ratio of the number of adults to children is (3x + y) : (x + 3y), where x represents the number of males and y represents the number of females.