Question 264862: The sum of the average number of times a man, a woman, and a one-year old child cry each month is 71.7. A one-year old cries 46.4 more times than a man. The average number of times a one-year old child cries a month is 28.3 more than the average number of times combined that a man and a woman cry. What is the average number of times per month that each cries?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! m = average times a man cries in a month.
w = average times a woman cries in a month.
c = average times a 1 year old child cries in a month.
I will examine each of the statements individually.
they are:
The sum of the average number of times a man, a woman, and a one-year old child cry each month is 71.7.
The first statement is clear. The formula would be:
m + w + c = 71.7
A one-year old cries 46.4 more times than a man.
The second statement is also clear. The formula would be:
c = 46.4 * m
The average number of times a one-year old child cries a month is 28.3 more than the average number of times combined that a man and a woman cry.
The 28.3 more than part is ok.
The average number of times combined I take to mean that I take the average number of times the man cries and the average number of times the woman cries and combine them to get an overall average that they both cry.
Based on that understanding, the formula for that statement becomes:
c = (m+w)/2 + 28.3
What is the average number of times per month that each cries?
based on my understanding, I have the following formulas:
m = m
c = 46.4*m
c = (m+w)/2 + 28.3
from the second and third formula, we can find w.
since they both equal to c, then they both equal to each other, so we have:
46.4*m = (m+w)/2 + 28.3
multiply both sides of this equation by 2 to get:
92.8*m = m + w + 56.6
subtract m from both sides of this equation and subtract 56.6 from both sides of this equation to get:
w = 92.8*m - m - 56.6
simplify this equation to get:
w = 91.8*m - 56.6
the equations we now have to work with are:
m = m
c = 46.4*m
w = 91.8*m - 56.6
m + w + c = 71.7
we take the equivalent values of all variables in terms of m to get:
m + 91.8*m - 56.6 + 46.4*m = 71.7
we add 56.6 to both sides of this equation and we combine like terms to get:
139.2*m = 128.3
we divide both sides of this equation by 139.2 to get:
m = .921695402
w = 91.8*m - 56.6 = 28.01163793
c = 46.4*m = 42.76666666
m + w + c = 71.7 confirming that these values are good.
the questions is:
what is the average number of times per month that each cries.
the answer is:
the man cries an average of .921695402 times per month.
the woman cries an average of 28.01163793 times per month.
the child cries an average of 42.76666666 times per month.
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