SOLUTION: The average weight for a group of 20 women is 130 pounds. If the average weight for 3/4 of these women was 140 pounds, what was the average weight, in pounds, for the rest of the

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Question 83718: The average weight for a group of 20 women is 130 pounds. If the average weight for 3/4 of these women was 140 pounds, what was the average weight, in pounds, for the rest of the women?
I know the answer is 100 but I can't figure out how I got. It might not be 100?
Found 2 solutions by checkley75, stanbon:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
TOTAL WEIGHT OF ALL WOMEN=20*130=2600 POUNDS.
3/4 OR .75 OF THE WOMEN AVERAGE 140 POUNDS. THUS THEY ACCOUNT FOR:
.75*20*140=2100 POUNDS.
THAT LEAVES 2600-2100=500 POUNDS TO DISTRIBUTE AMONG THE REMAINING 1/4 OF THE WOMEN.
1/4*20*X=500 (X BEING THE AVERAGE WEIGHT OF THE REMAINING 1/4.
5X=500
X=500/5
X=100 POUNDS IS THE AVERAGE WEIGHT OF THE REMAINING 1/4.
PROOF
3/4*20*140+1/4*20*100=2600
2100+500=2600
2600=2600

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The average weight for a group of 20 women is 130 pounds. If the average weight for 3/4 of these women was 140 pounds, what was the average weight, in pounds, for the rest of the women?
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Total weight of the group divided by # in the group has to be 130 lbs.
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Total weight = (3/4)(20)(140) + (1/4)(20)x
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EQUATION:
(15*140+5x)/20 = 130
2100 + 5x = 2600
5x = 500
x= 100
The average wt. of the remaining (1/4)th of the group is 100 lbs.
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Cheers,
Stan H.