https://file.aiquickdraw.com/mathbot/file/1726306063127gr51nfkd.jpg

Let's solve question 4 based on the image you uploaded, which involves ferry A and ferry Z. Here's the breakdown:

### Given Data:

- **Stem-and-leaf plot** of passengers traveling on Ferry A and Ferry Z over a 14-day period.

The data presented can be interpreted as follows:
- **Ferry A:** $ 8, 7, 6, 7, 6, 6, 6, 5, 5, 5, 4, 4, 3, 3 $
- **Ferry Z:** $ 2, 0, 0, 5, 8, 6, 3, 3, 4, 5, 7, 7, 7, 9 $

#### Part (a): 
How many more passengers traveled on Ferry Z than on Ferry A?

We need to sum the total passengers on both ferries and compare.

- **Ferry A Sum:** $ 8 + 7 + 6 + 7 + 6 + 6 + 6 + 5 + 5 + 5 + 4 + 4 + 3 + 3 = 75 $
- **Ferry Z Sum:** $ 2 + 0 + 0 + 5 + 8 + 6 + 3 + 3 + 4 + 5 + 7 + 7 + 7 + 9 = 66 $

Difference: $ 75 - 66 = 9 $

So, **9 more passengers** traveled on Ferry A than on Ferry Z.

---

#### Part (b): 
The cost of a trip on Ferry A is \$12.50 and on Ferry Z is $ Sx $. The takings on Ferry Z were \$3.30 less than on Ferry A over this period. Find the value of $ x $.

To calculate this:
1. **Total cost on Ferry A** = $ 75 \times 12.50 = 937.50 $ dollars.
2. Let the cost on Ferry Z be $ Sx $, then the total revenue from Ferry Z is $ 66 \times Sx $.
3. The condition says that the takings on Ferry Z were \$3.30 less than Ferry A, so:
   \[
   66 \times Sx = 937.50 - 3.30 = 934.20
   \]
4. Solve for $ x $:
   \[
   Sx = \frac{934.20}{66} \approx 14.15
   \]

Thus, the value of $ x $ is approximately **14.15**.

---

#### Part (c): 
Find the least and greatest possible number of days on which the two ferries could have carried exactly the same number of passengers.

From the stem-and-leaf plot, check for days where the number of passengers on both ferries was the same:

- **Same number of passengers:**
  - Day 7: Both ferries had **5** passengers.
  - Day 8: Both ferries had **7** passengers.

Thus, the ferries carried the same number of passengers on **2 days**.

---

Would you like further details or clarifications? Here are some follow-up questions:

1. How would you calculate the average number of passengers on Ferry A?
2. What is the total revenue generated by both ferries combined?
3. If the cost of a trip on Ferry A increased by 10%, what would be the new revenue for Ferry A?
4. On which day was the maximum number of passengers on Ferry Z?
5. How would the result change if 5 more passengers traveled on Ferry Z?

**Tip**: Always verify conditions when interpreting stem-and-leaf plots, as each stem represents a range of values.

Over a 14-day period, data were collected on the number of passengers traveling on two ferries, A and Z. The results are presented in a stem-and-leaf diagram. Part (a) asks how many more passengers traveled on ferry Z than on ferry A. Part (b) asks to find the value of x, where the cost of a trip on ferry A is $12.50 and ferry Z is Sx, given that the takings on ferry Z were $3.30 less than on ferry A. Part (c) asks to find the least and greatest possible number of days on which the two ferries could have carried exactly the same number of passengers.

Solve a ferry passenger problem using a stem-and-leaf diagram. Learn how to calculate the difference in passengers, revenue, and solve for unknown values in algebraic equations. Ideal for students in Grades 6-8.

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