Question

Select the correct answer.

Amir is starting a stamp collection. After 3 weeks he has collected 35 different stamps, and after 9 weeks he has collected 105 different stamps. If Amir keeps collecting stamps at this same rate, how many stamps will he have after 15 weeks?

A.
140
B.
175
C.
210
D.
245

Answer 1

To find out how many stamps Amir will have after 15 weeks, we first need to determine the rate at which he is collecting stamps.

From the information given:
- After 3 weeks, Amir has 35 stamps.
- After 9 weeks, Amir has 105 stamps.

Let's calculate the number of stamps he collects in a week:

1. **From 3 to 9 weeks:**
- The time span is \(9 - 3 = 6\) weeks.
- The number of stamps collected during this period is \(105 - 35 = 70\) stamps.

Therefore, the rate of collecting stamps per week is:

\[
\text{Rate} = \frac{70 \text{ stamps}}{6 \text{ weeks}} = \frac{35}{3} \text{ stamps/week} \approx 11.67 \text{ stamps/week}
\]

2. **Verifying the rate over the first 3 weeks:**
- In the first 3 weeks, Amir collected 35 stamps.
- Thus, the average rate over these 3 weeks is:

\[
\text{Average Rate} = \frac{35 \text{ stamps}}{3 \text{ weeks}} \approx 11.67 \text{ stamps/week}
\]

Now, since we have confirmed that Amir collects stamps at a rate of \(\frac{35}{3}\) (or approximately \(11.67\)) stamps per week, we can now calculate how many stamps he will have after 15 weeks:

\[
\text{Total Stamps after 15 weeks} = \text{Rate} \times \text{Time}
\]
\[
\text{Total Stamps} = \left(\frac{35}{3} \text{ stamps/week}\right) \times 15 \text{ weeks}
\]

Calculating that gives:

\[
= \frac{35 \times 15}{3} = \frac{525}{3} = 175
\]

Thus, Amir will have **175 stamps** after 15 weeks.

The correct answer is **B. 175**.