A mobile phone company offers two plans: Option A and Option B. The cost for Option A includes a fixed monthly fee plus a per-minute charge. The cost for Option B is purely a per-minute charge. The ta

Using points $(0, 150)$ and $(50, 230)$ from the table:

The tariff for Option A is R1.60 per minute.

Using points $(0, 0)$ and $(50, 125)$ from the table:

The tariff for Option B is R2.50 per minute.

The general form is $C = mM + c$, where $C$ is total cost, $M$ is minutes, $m$ is the tariff per minute, and $c$ is the fixed cost.
For Option A, $m = 1.6$ and $c = 150$.

For Option B, $m = 2.5$ and $c = 0$.

Substitute $M = 100$ into the equation for Option A:

The cost for Option A is R310.

Substitute $M = 100$ into the equation for Option B:

The cost for Option B is R250.

Since R250 < R310, Option B will be the cheapest option for 100 minutes of calls.

Option A becomes cheaper than Option B when $C_A < C_B$. The point where they are equal is the intersection:

So, approximately 167 minutes.

Using $M \approx 166.67$ in either equation:

At approximately $(167 \text{ minutes}, 417 \text{ R})$, Option A becomes cheaper than Option B.