## 98. Weighing the Child.

- Last summer I witnessed a funny incident at a railway station, said my friend. - A small family stood in front of the automatic scales, which were calibrated for 200 pounds, trying in vain to solve the difficult problem of weighing the child. As soon as the parents left the child alone on the scales, he would start crying and jump off, and the father had to hold the dog, which also wanted to participate in this operation. Finally, the father, together with the child and Fido, climbed onto the scales, and I took a photo of them.

At this point, my friend showed me the photo, from which I copied only the scale reading, as the rest did not interest me (see the figure).

- After that, the man turned to his wife and said, "I think, dear, that together with the child I weigh 162 pounds more than the dog, and the dog weighs 70% less than the child. We should think it over at home."

I also wanted to figure it out for myself. What do you think the cute child weighed?

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-032.jpg?height=471&width=483&top_left_y=1980&top_left_x=798)
98. It is important to note that the father, child, and dog together weighed 180 pounds, as shown in the figure. Further, the difference between 180 and 162 is 18, which matches twice the weight of the dog. Therefore, the dog weighs 9 pounds, and the child 30 pounds, since if you subtract \(70\%\) of this weight from 30 pounds, you get exactly 9.
\footnotetext{
* One can agree with the author's statement only with great reservation. Indeed, the scales in the figure appear to be in balance with unequal (the right one is longer) lever arms, which precisely means that the pans have different weights! In favor of the author's interpretation is the fact that the pans look the same, and thus weigh the same. But then one must assume that the scales are not depicted in a position of equilibrium but are passing through the point of equilibrium. In a moment, the right pan will begin to descend. Perhaps, instead of appealing to the figure, the author should have simply analyzed the two cases presented.
}