B1 For mobile phone calls, Jane uses a package that is characterized by a uniform price for calls to all networks in Slovenia. Therefore, her monthly bill for mobile phone calls depends on the monthly subscription fee and the number of minutes of her outgoing calls. In September, she had 75 minutes of outgoing calls. The bill amounted to 15.45 euros. In October, she paid 20.01 euros for 113 minutes. What is the monthly subscription fee and the cost per minute of the call?
B1. I. method

We determine that the phone bill is equal to the value of the linear function $f(x)=k \cdot x+n$, where $k$ is the cost per minute of conversation, $x$ is the number of minutes of conversation, and $n$ is the monthly subscription fee. We are given two values of this function: $f(75)=15.45$ and $f(113)=20.01$. We calculate $k=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}=\frac{20.01-15.45}{113-75}=\frac{4.56}{38}=0.12$. We consider $f\left(x_{2}\right)-f\left(x_{1}\right)=k \cdot\left(x_{2}-x_{1}\right)$ and substitute the appropriate data. We get $f(x)=0.12 \cdot x+6.45$. $n$ can be calculated from the relationship $f(x)=l \cdot x+n$. We substitute the data from $f(75)=15.45$ and get $15.45=0.12 \cdot 75$. We calculate $n=6.45$. Therefore, a minute of conversation costs 0.12 euros and the monthly subscription is 6.45 euros.

I. method

Determination that the phone bill is equal to the value of the linear function ................... 1 point Noting or considering $f(75)=15.45$ and $f(113)=20.01 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .1$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-12.jpg?height=51&width=1670&top_left_y=2499&top_left_x=233)$\qquad$ Answer: A minute of conversation costs 0.12 euros and the monthly subscription is 6.45 euros........ 1 point

II. method

We conclude: In October, Jana spoke 38 minutes more and paid 4.56 euros more. Therefore, 1 minute of conversation costs $4.56: 38=0.12$ euros. Considering the bill for September as well, we get the monthly subscription of 6.45 euros.

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-13.jpg?height=51&width=1685&top_left_y=423&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-13.jpg?height=52&width=1687&top_left_x=230)

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-13.jpg?height=51&width=1685&top_left_y=523&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-13.jpg?height=58&width=1685&top_left_y=565&top_left_x=228)

Answer: A minute of conversation costs 0.12 euros and the monthly subscription is 6.45 euros....... 1 point NOTE: A student who arrives at the correct solution through logical reasoning and performs a check gets all possible points.