Math worksheet with Australian-themed word problems for students.

Here are the solutions to the problems on the worksheet, solved step-by-step.

1. Kangaroo Jump
* Step 1: Find the length of the kangaroo's body in terms of $x$. The problem says the jump ($x$) is 3 times the body length. So, Body Length = $\frac{x}{3}$.
* Step 2: The question asks for the jump distance if it can jump *twice* its body length.
* Step 3: Calculate: $2 \times (\text{Body Length}) = 2 \times \frac{x}{3} = \frac{2x}{3}$.
* Answer: $\frac{2x}{3}$ meters (or $\frac{2}{3}x$).

2. Sydney Opera House Attendance
* Step 1: Identify the previous month's visitors: $y$.
* Step 2: "Twice the number" means $2y$.
* Step 3: "200,000 more than" means we add 200,000.
* Answer: $2y + 200,000$

3. Koala Population
* Step 1: Start with 500 koalas.
* Step 2: Decreasing by 10% each year means 90% remain. We multiply by $0.9$ for every year that passes.
* Step 3: After $t$ years, we multiply by $0.9$, $t$ times.
* Answer: $500(0.9)^t$

4. Sydney Harbour Bridge Height
* Step 1: Use the form $y = mx + b$.
* Step 2: $b$ is the starting height at the center ($x=0$), which is 134 meters. So, $b = 134$.
* Step 3: The height drops 5 meters for every kilometer. This is a negative slope. So, $m = -5$.
* Answer: $y = -5x + 134$

5. Great Barrier Reef Diving Depth
* Step 1: Use the equation $d = 10x + 5$.
* Step 2: Substitute the distance $x = 40$ into the equation.
* Step 3: Calculate: $d = 10(40) + 5$.
* Step 4: $d = 400 + 5 = 405$.
* Answer: 405 meters

6. Ayers Rock Circumference
* Step 1: The circumference is 5 times the radius ($r$). So, Circumference = $5r$.
* Step 2: Cost is $c$ dollars per meter.
* Step 3: Total cost = Price per meter $\times$ Total meters.
* Answer: $c = 5rc$ (or just $5rc$)

7. Melbourne Tram Fare
* Step 1: The first 5 km cost a flat rate of $\$2.50$.
* Step 2: Any distance beyond 5 km is $(k - 5)$.
* Step 3: The extra cost is $\$0.20$ for each of those extra kilometers: $0.20(k - 5)$.
* Step 4: Add the base fare and the extra fare.
* Answer: $c = 2.50 + 0.20(k - 5)$

8. Gold Coast Theme Park Tickets
* Step 1: Base cost for 3 people is $\$30$.
* Step 2: Extra people beyond 3 is $(n - 3)$.
* Step 3: Extra cost is $\$5$ for each extra person: $5(n - 3)$.
* Step 4: Add the base cost and extra cost.
* Answer: $c = 30 + 5(n - 3)$

9. Perth Bus Travel Time
* Step 1: The formula for time is $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$.
* Step 2: Distance is $d$ and Speed is 60.
* Answer: $t = \frac{d}{60}$

10. Uluru Sunset Time
* Step 1: We need to find the minutes past 6:00 PM when the sun sets at 7:00 PM.
* Step 2: From 6:00 PM to 7:00 PM is exactly 60 minutes. So, set $t = 60$.
* Step 3: Use the equation: $60 = 4m + 120$.
* Step 4: Subtract 120 from both sides: $-60 = 4m$.
* Step 5: Divide by 4: $m = -15$.
* *(Note: A negative result implies that according to this specific mathematical model, the sunset occurred 15 minutes before 6:00 PM, or the model is only valid for dates earlier in the year. However, mathematically, the value for m is -15).*
* Answer: -15

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Final Answer:
1. $\frac{2x}{3}$
2. $2y + 200,000$
3. $500(0.9)^t$
4. $y = -5x + 134$
5. 405 meters
6. $5rc$
7. $c = 2.50 + 0.20(k - 5)$
8. $c = 30 + 5(n - 3)$
9. $t = \frac{d}{60}$
10. -15