SOLUTION: The average weight of a group of children is 100 pounds. Trisha, who weighs 112 pounds, then join the group. This raises the average weight of the group to 102 pounds. How many chi

Algebra ->  Average -> SOLUTION: The average weight of a group of children is 100 pounds. Trisha, who weighs 112 pounds, then join the group. This raises the average weight of the group to 102 pounds. How many chi      Log On


   

Question 67574: The average weight of a group of children is 100 pounds. Trisha, who weighs 112 pounds, then join the group. This raises the average weight of the group to 102 pounds. How many children were in the original group?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the average weight of a group of children is 100 pounds. Trisha, who weighs 112 pounds, then join the group. This raises the average weight of the group to 102 pounds. How many children were in the original group?
:
Let x = number of children in the original group
Let y = the total weight of the original children
:
Before Trisha equation:
y%2Fx+=+100
:
Multiply equation by x and have:
y = 100x
:
After Trisha equation:
%28%28y%2B112%29%29%2F%28%28x%2B1%29%29 = 102
:
Substitute 100x for y and we have:
%28%28100x%2B112%29%29%2F%28%28x%2B1%29%29 = 102
:
Multiply equation by (x+1) and have:
100x + 112 = 102(x+1)
:
100x + 112 = 102x + 102
:
112 - 102 = 102x - 100x
10 = 2x
x = 5 kids in the original group:
:
Check: %28%28500+%2B+112%29%29%2F6 = 102