Alea was too busy dwelling on her terrible fate to question what Oluse was asking her to do. She owed him money, and she couldn't pay. She would pretty much have to do whatever he asked. Hurrying to follow his instructions, she found the jar, and the linen pouches. When she got to the scale, she hesitated. She had never used one of these before. How did it work?
After a moment of panic, a vague memory floated to the surface of her mind. She thought she recalled a demonstration of this device on one of the more boring days at the Academy. The small objects of various sizes but similar shapes sitting next to the scale had something to do with it, she remembered.
Upon closer examination, she realized the objects had numbers on them. She picked up one that said "1" on it. But what was "point seven five"? From her vague memory, it sounded like... part of a number? So... she was looking for a weight that was smaller than the "1". She picked one about half the size. The label said "5", which really confused Alea. The next smallest size said "25". This was madness. Alea must be missing something. What was she missing?
She peered closer at all three objects, trying to find any distinguishing marks that would make this make sense. All she could find was that the "1" was missing the dot that the other two had. Wait... dot...point...did the dot have something to do with making it part of a number? Alea had to stand still for a moment as more connections were making sense in her brain. When was 5 half of 1? 5 silver mizas were half of 1 miza. But what about the 25?
That one was going to be trickier. What if she just added the numbers with dots on them? 25 plus 5 was... 30. But was that right? She tried thinking about it in terms of money again. If the 25 was less than one...
Alea's brain was beginning to hurt. There had to be a better way to do this. Think again in terms on wholes and parts. The whole is greater than the part, was the first thing she ever learned in math, which she was able to remember mostly because it was so obvious. Except right now... No, she could do this! The "1" was the whole. She placed that on one side of the scale. That side sank. Okay so far. The "5" was a part. She placed that on the other side of the scale. It tipped, but not enough to bring it back to the same height.
Now, logically, if the "5" was half of the whole, then two of them should be the same as a whole, right? She found another "5" and placed it next to the first one, feeling rather gleeful as her prediction was rewarded with the scale returning to balance. She took all the weights off to start over. She placed the "5" on one side. The "25" looked about half as big as the "5", so she put two of them on the other side, confirming her suspicions. So "25" was half of "5". Well, if she did the math, what was half of 5? You couldn't divide 5 in half, because it was odd... but half of four was two, and half of one was a half... so that should make half of 5 be 2 and a half... and she had just decided that the 5 was a half, so, 2 and a half... 2 and a 5... 25... it was all starting to make a crazy sort of sense!
Okay, so how did she get point seven five from that? This stumped her, and she spent a few seconds just starting at the weights. Then she had a crazy idea... what if she lined up the points? That put the 5 over the 2 in 25... which sort of made sense. The "5" was half of the whole, but the 5 in the "25" was half of THAT, which was just a whole new level of half. So if she added them that way, that made... point seven five. Exactly what she was looking for and she had it in her hands the whole time.
She was so glad she had finally figured it out that she lost all immediate interest in math. She put the three weights on one side of the scale, and one of the pouches on the other. She either didn't notice or didn't care at this point that the pouch also had some weight, but she filled it with careful scoops of powder. One full pouch did not bring the scale back into balance, so she added another pouch and filled that one nearly as full. When the scales looked to be roughly balanced again, Alea silently declared herself finished, and cleared the scales before Oluse could tell her she had done it wrong and needed to fix it.
Once she had the two pouches in hand, she stared at them in confusion. What was she doing again? She had missed the entirety of Oluse's mumbling, to the point that she didn't even realize he was deliberately manipulating the price for her. She numbly accepted the miza and paper, still not entirely sure what had just happened. Her brain felt like is was stretching against her skull, and she wasn't sure she could think normally anymore.