Help about Arithmetic mean!

**Mat724** · May 28th 2012, 02:08 PM

Ok, its a word problem and i am struggling so much with it... i know the answer, which is 2/7 or .285... idk how to do it. please help

One adult and 10 children are in an elevator. If the adult's weight is 4 times the average (arithmetic mean) weight of the children, then the adult's weight is what fraction of the total weight of the 11 people in the elevator?

**HallsofIvy** · May 28th 2012, 02:23 PM

Let "w" be the average weight of the children. So the adult's weight is 4w. The total weight of the 10 children is 10w. So what is the total weight of the adult and children? What is the ratio of the adults weight to that total weight?

**Soroban** · May 28th 2012, 05:41 PM

Hello, Mat724!

One adult and 10 children are in an elevator.
If the adult's weight is 4 times the average (arithmetic mean) weight of the children,
then the adult's weight is what fraction of the total weight of the 11 people in the elevator?

Let $A$ = weight of the adult.
Let $C$ = total weight of the children.
Then $\tfrac{C}{10}$ = the average weight of the children.

We are told: $A \:=\:4\left(\tfrac{C}{10}\right) \quad\Rightarrow\quad A \:=\:\tfrac{2}{5}C$

Then the total weight of the 11 people is: . $A + C \:=\:\tfrac{2}{5}C + C \:=\:\tfrac{7}{5}C$

The desired fraction is: . $\frac{\text{adult}}{\text{total}} \;=\; \frac{\frac{2}{5}C}{\frac{7}{5}C} \;=\;\frac{2}{7}$

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