Three numbers are such that when the average of any two is added to the third, the results are 200, 180, and
160. What is the average of the three numbers?

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Accepted Answer

1. Let the numbers be $x,y,z$. We have:

- $\frac{x+y}{2}+z=200$
- $\frac{x+z}{2}+y=180$
- $\frac{y+z}{2}+x=160$

2. Multiply each equation by 2:

- $x+y+2z=400$
- $x+2y+z=360$
- $2x+y+z=320$

3. Add them: $4(x+y+z)=1080$, so $x+y+z=270$.

4. The average is $\dfrac{270}{3}=90$. **Answer: 90.**

FINAL_ANSWER: c

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Answer

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