1550.26 – Brick on a 2-Pan Scale

While watching a demonstration of how a 2-pan scale works, we notice that a brick placed on one side exactly balances 34\dfrac{3}{4} of a kg plus 34\dfrac{3}{4} of a brick on the other side. If this is so, what does the brick weigh?

Solution

Let bb represent the weight of the brick.

Then b=34+34b  ⟹  4b=3+3b  ⟹  b=3b = \dfrac{3}{4} + \dfrac{3}{4b} \implies 4b = 3 + 3b \implies b = 3.

Check: 3=34+34⋅3=34+94=124=33 = \dfrac{3}{4} + \dfrac{3}{4} \cdot 3 = \dfrac{3}{4} + \dfrac{9}{4} = \dfrac{12}{4} = 3.

We, the Stella crew, try to make problems that might have some basis in reality. Alas, this is not such a problem. It is unimaginable that we would notice anything like what the problem claims we would notice within the context of a demonstration. Furthermore, we have been lax in neglecting to weigh an actual brick so as to use its real weight in the problem. Nonetheless, the problem is here, to be grappled with.