the average weight 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 th rest of the women?
20*120=15*140 + 5*W
solve for W
3/4 of the women is 20*3/4, or 15 women
If the average of all of the women is 130lbs, then the total weight is 20*130 = 2600lbs
The average of those 15 women is 140lbs. So 2600 - 15*140 is the weight left for the other 5 women.
2600 - 15*140 = 500
Find the average of those 5 women by dividing 500/5.
500/5 = 100lbs
100
To find the average weight for the rest of the women, we first need to determine the number of women who have a weight of 140 pounds.
We know that 3/4 of the women have a weight of 140 pounds. To find this number, we can multiply the total number of women by 3/4:
Number of women with a weight of 140 pounds = (3/4) * 20 = 15
Now we have 15 women weighing 140 pounds in total, and we want to find the average weight for the rest of the women. Therefore, we need to subtract these 15 women from the total of 20 women to find the number of women remaining:
Number of remaining women = total number of women - number of women with a weight of 140 pounds
Number of remaining women = 20 - 15 = 5
Now that we know there are five women remaining, we can calculate their average weight. We know the average weight of all 20 women is 130 pounds, so we can find the total weight of the 20 women:
Total weight of all 20 women = average weight * number of women
Total weight of all 20 women = 130 * 20 = 2600 pounds
Next, we subtract the total weight of the 15 women (15 women * 140 pounds):
Total weight of the rest of the women = total weight of all 20 women - total weight of 15 women
Total weight of the rest of the women = 2600 - (15 * 140) = 2600 - 2100 = 500 pounds
Finally, to find the average weight for the rest of the women, we divide the total weight of the rest of the women by the number of remaining women:
Average weight for the rest of the women = total weight of the rest of the women / number of remaining women
Average weight for the rest of the women = 500 / 5 = 100 pounds
Therefore, the average weight for the rest of the women is 100 pounds.