SOLUTION: Hi 15 girls and a number of boys collected an average of 28 stamps. The girls collected an average of 20 stamps. If each boy collected an average of 14 more stamps than each girl

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Question 1189190: Hi
15 girls and a number of boys collected an average of 28 stamps. The girls collected an average of 20 stamps. If each boy collected an average of 14 more stamps than each girl how many children were there.
Thanks
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you have 15 girls and x boys.
total of girls and boys = 15 + x.
x is the number of boys.

the girls average 20 stamps each.
the boys averaged 14 more each for a total of 34 each.

the average of the boys and the girls together is 28.

the equation you need to solve is:

20 * 15 + 34 * x = 28 * (15 + x)
simplify to get:
300 + 34 * x = 420 + 28 * x
subtract 28 * x from both sides of the equation and subtract 300 from both sides of the equation to get:
34 * x - 28 * x = 420 - 300
combine like terms to get:
6 * x = 120
solve for x to get:
x = 120 / 6 = 20

this says that the number of boys is 20.
15 girls plus 20 boys = 35 children.
15 * 20 + 20 * 34 = 300 + 680 = 980 collected stamps.
980 / 35 = average of 28 stamps per child.

numbers look good.
solution is that there were 35 children.





Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
15 girls and a number of boys collected an average of 28 stamps. The girls collected an average of 20 stamps. If each boy collected an average of 14 more stamps than each girl how many children were there.
Thanks 
Let number of children be C
As there were 15 girls, number of boys = C - 15
With average number collected by girls being 20, total collected by girls = 15(20) = 300
With average number collected by boys being 14 more than each girl's average collection, or 34 (20 + 14),
total collected by boys = 34(C - 15) = 34C - 510
Since average number collected was 28, we get: 300 + 34C - 510 = 28C
300 - 510 = 28C - 34C
- 210 = - 6C
Number of children, or