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average birthdays

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At the classroom costume party the average age of the (b) boys is g and the average age of the (g) girls is b. If the average age of everyone, including the 42-year-old teacher, is b+g, what is the value

of b+g?

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Posted (edited) · Report post

1) sum of ages=boys+girls+teacher=b*g+g*b+42=2*b*g+42


2) sum of ages=average_age*number_of_persons=(b+g)*(b+g+1)

1=2: 2*b*g+42=(b+g)*(b+g+1)

I fed it into Wolfram Alpha and got no positive integer (number of persons) solution.

A small program to be sure:

for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)

(b,g)=(3,5) => b+g=8

I would be interested if someone finds the solution with Wolfram Alpha.

Sorry, unable to hide.
Edited by bonanova
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Posted · Report post

i found two positive integer answers

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Posted (edited) · Report post

Yes, I should have started at 0. (a,b)=(0,6) -> (a+b)=6

Edited by bonanova
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