Question: The Miss Petra Psychic Hotline charges $5 for the first minute and $2 for each additional minute. Let $C$ represent the total cost of a call and $M$ represent the number of minutes that the call lasted.
i) Give an equation that describes the situation.
ii) Determine the cost of a 15 minute call.
Options:
i) $C = 2M$
ii) The cost of a 15 minute call is 30.
i) $C = 5 + 2M$
ii) The cost of a 15 minute call is 33.
i) $C = 5 + 2(M - 1)$
ii) The cost of a 15 minute call is 33.
i) $C = 5 + 2M$
ii) The cost of a 15 minute call is 35.
1. **State the problem:**
We need to find an equation for the total cost $C$ of a call lasting $M$ minutes, where the first minute costs 5 and each additional minute costs 2.
2. **Formulate the equation:**
- The first minute costs $5$.
- Each additional minute (i.e., $M - 1$ minutes) costs $2$ each.
So the total cost is:
$$C = 5 + 2(M - 1)$$
3. **Simplify the equation:**
$$C = 5 + 2M - 2 = 3 + 2M$$
4. **Calculate the cost for a 15-minute call:**
Substitute $M = 15$:
$$C = 5 + 2(15 - 1) = 5 + 2 \times 14 = 5 + 28 = 33$$
5. **Check other options:**
- $C = 2M$ gives $C = 2 \times 15 = 30$, which ignores the first minute cost.
- $C = 5 + 2M$ gives $C = 5 + 2 \times 15 = 35$, which charges for 16 minutes.
6. **Conclusion:**
The correct equation is:
$$C = 5 + 2(M - 1)$$
and the cost for a 15-minute call is:
$$33$$