Three numbers are such that when the sum of any two of them is added to one-fourth of the third, the results are 156, 148, and 140 respectively. What is the average of the three numbers?

Question

Accepted Answer

1. Let the numbers be $x,y,z$ and set $S=x+y+z$.

2. Add the three given equations:  
$$(x+y)+(y+z)+(z+x)+	frac14(x+y+z)=156+148+140$$  
So $2S+	frac14S=	frac94S=444$.

3. Solve for $S$: $S=444	imes	frac{4}{9}=	frac{592}{3}$. The average is $S/3=	frac{592}{9}\approx65.77$.

4. Thus the correct choice is (c).

FINAL_ANSWER: c

Answer

Answer

Answer