The real numbers x, y and z satisfy the equations x+2y+3z=950 and 3x+2y+z=1450. What is the average of x, y and z?
+53 \(\text{Add the two equations together to get }\)\(4(x+y+z)=2400, \text{thus } x+y+z=600.\)\( \text{ Because we have 3 numbers, we divide}\)\(\text{this by 3 to get the average:} \frac{x+y+z}{3}=\boxed{200.}\)
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