Unknown weights

Picture an old shop तराजू — a pan balance with two plates. Here is such a weighing scale, and the numbers on it represent the same units of weight. The scale BALANCES, which tells you something exact: the total weight on the left plate equals the total weight on the right.

That single fact is enough to find weights you were never told. If one plate holds three slices of bread, each of weight 2, and the other holds two fried eggs, then the two eggs together weigh 2 + 2 + 2 = 6, so one egg weighs 3.

Some of these are straightforward. Others need a trick, and here it is: If we remove equal weights from both plates, the scale stays balanced. Taking the same amount off each side cannot tip it.

Look at a scale where all the sacks have the same unknown weight, and there is a sack on BOTH plates. Remove one sack from each plate. The scale is still balanced, and now there is one fewer unknown to worry about.

The other strategy is to ask: can I remove objects so that the sacks are only on ONE plate? If every sack ends up on the left and only known weights on the right, the answer is staring at you.

Discuss your answers with your classmates, and give REASONS why you think your answer is right. Different people find these by different routes — one removes weights, another counts up — and comparing the methods is as useful as getting the number.

Everything in this chapter grows from this one scale. A balance that must stay balanced is exactly what an equation is.