Camel Zakāt

# The Equation

$$
x - 40a - 30b
$$

| Variable | Meaning           |
| -------- | ----------------- |
| $x$      | no. of camels     |
| $a$      | no. _bint labūns_ |
| $b$      | no. of _ḥiqqahs_  |

$a$ has to be the highest possible number.
$b$ has to be the lowest possible number.
The smallest remainder needs to be achieved.

# The Data

| $x$ | $a$ | $b$  | Condition                |
| --- | --- | ---- | ------------------------ |
| 120 | (3) | (4)  | Choose either $a$ or $b$ |
| 130 | 1   | 3    |                          |
| 140 | 2   | 2    |                          |
| 150 | 3   | 1    |                          |
| 160 | 4   | 0    |                          |
| 170 | 2   | 3    |                          |
| 180 | 3   | 2    |                          |
| 190 | 4   | 1    |                          |
| 200 | 5   | 0    |                          |
| 210 | 3   | 3    |                          |
| 220 | 4   | 2    |                          |
| 230 | 5   | 1    |                          |
| 240 | (8) | (6)  | Choose either $a$ or $b$ |
| 250 | 4   | 3    |                          |
| 260 | 5   | 2    |                          |
| 270 | 6   | 1    |                          |
| 280 | 7   | 0    |                          |
| 290 | 5   | 3    |                          |
| 300 | 6   | 2    |                          |
| 310 | 7   | 1    |                          |
| 320 | 8   |      |                          |
| 360 | (9) | (12) | Choose either $a$ or $b$ |