This has nothing to do with Sage as a math tool ; it is a elementary school arithmetic applied to elementary school economics.

Elements of your problem :

- the production cost (35200 in your example)
- sales price (269100 in your example.

Now for some *definitions* (there I may be wrong, not being versed in englis-langiuage economics ; take my word wot a grain of salt (or even a toin of salt...)) :

- profit = sales price - production cost.
- profit
*rate* = profit/production cost. - profit
*margin* = profit/sales price.

To work the numerical results, Sage is about as necessary as a howitzer to kill a fly. Nevertheless :

Enter the data :

```
sage: production_cost = 32500
sage: sales_price = 269100
```

Work out the results :

```
sage: profit = sales_price - production_cost ; profit
236600
sage: profit_rate = profit/production_cost ; profit_rate
182/25
```

Note that Sage tends to give you "exact" results whenever possible ; in this case, a fraction. Since this is not easy to use for most people, we convert this fraction to a decimal expression by usong the *method* `.n`

:

```
sage: profit_rate = (profit/production_cost).n() ; profit_rate
7.28000000000000
```

Meaning that your profit is 7.28 *times* your initial investment. Bloody unrealistic...

```
sage: profit_margin=(profit/sales_price).n() ; profit_margin
0.879227053140097
```

The profit margin is about 0.88, meaning that for each unit of your sales, 0.88 of this unit goes to your profit. Bloody unlikely again...

It is customary to express this margin (and your profit rate too, BTW) in so-called *percentage*, which is a fraction multiplied by 100 :

```
sage: profit_margin_pct=profit_margin*100 ; profit_margin_pct
87.9227053140097
```

meaning that for 100 units of sales, about 89 go tou your profit.

*Important :* Note that any competent school teacher would (rigtfully !!!) yell at me for not expressing my data and results with their **units** ; my physics professors in high school would have fainted... And here is acouple of important facts :

- costs and prices
*must* have the same units for the addition/substraction to have a meaning ; - rates and margin
*have no unit* (they are "dimensionless numbers", important concept in economics and in physics, for different reasons : their value is *independent* of your unit system).

Now, I'd suggest you to get textbooks of elementary arithmetic and elementary economics, working them with a hand calculator (or even a slide rule, if you still can get one outside of a museum...). Sage will become useful *later*...