18. Weighing the baby at the clinic was a problem. The baby would not keep still and caused the scales to wobble. So I held the baby and stood on the scales while the nurse read off $78 \mathrm{~kg}$. Then the nurse held the baby while I read off $69 \mathrm{~kg}$. Finally I held the nurse while the baby read off $137 \mathrm{~kg}$. What was the combined weight of all three ?
A $142 \mathrm{~kg}$
B $147 \mathrm{~kg}$
C $206 \mathrm{~kg}$
D $215 \mathrm{~kg}$
E $284 \mathrm{~kg}$
(This problem appeared in the first Schools' Mathematical Challenge in 1988 - 25 years ago.)
Solution: $\mathbf{A}$
We let the weights of the baby, the nurse and myself be $x \mathrm{~kg}, y \mathrm{~kg}$ and $z \mathrm{~kg}$, respectively. The information we are given implies that $x+z=78, x+y=69$ and $y+z=137$. Adding these three equations gives $(x+z)+(x+y)+(y+z)=78+69+137$, that is, $2 x+2 y+2 z=284$. It follows that $x+y+z=142$. So the combined weight of all three was $142 \mathrm{~kg}$.