1. Tone filled the fuel tank to the top and set off on a long journey. The data he read from the car's electronic display are shown in the table.

| kilometers | 35824 | 36149 | 36449 |
| :--- | :--- | :--- | :---: |
| fuel data | consumption $17.2 \ell$ | consumption $39.3 \ell$ | remaining $5.3 \ell$ |

What is the capacity of the fuel tank of this car?

NOTE: Assume that the car has a constant fuel consumption per kilometer.
1. I. method:

We determine that fuel consumption is a linear function of the kilometers driven, $f(x)=k \cdot x$. We calculate $k=\frac{39.3-17.2}{36149-35824}=\frac{22.1}{325}=6.8$ liters per 100 kilometers. For an additional 300 kilometers, the consumption is $f(300)=0.068 \cdot 300=20.4 \ell$. Adding up $39.3+20.4+5.3=65 \ell$.

Determination of linear dependence 1 point

Calculation $k=\frac{39.3-17.2}{36149-35824}=\frac{22.1}{325}=6.8$ ... 2 points

Calculation of fuel consumption for $300 \mathrm{~km} f(300)=0.068 \cdot 300=20.4 \ell$ ... 1 point

Calculation of tank volume $39.3+20.4+5.3=65 \ell$ ... 1 point

Answer ..........................................................................................................

II. method:
We consider direct proportionality.

| initial amount $x$ | $x-17.2$ | $x-39.3$ | 5.3 |
| :--- | :--- | :--- | :--- |
| distance in km | 35824 | 36149 | 36449 |

We write the final calculation

22.1

325

We calculate $x=65 \ell$.

Determination of direct proportionality ...............................................................................................................

Writing the table .......................................................................................................................................

Writing the final calculation ........................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_6d1b766ff5bddd57ba61g-09.jpg?height=55&width=1636&top_left_y=1326&top_left_x=210)

Answer .........................................................................................................