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The image shows a math problem related to the cost of renting a jet ski at two different beaches: a northern beach and a southern beach. Here’s the breakdown of the problem:

### Part a) Equations for the cost of renting a jet ski:
- **Northern beach:**
  The cost to rent a jet ski is $20 as a base fee, plus $12 per hour.
  So, the equation for the cost $ C $ after renting for $ t $ hours is:
  \[
  C = 20 + 12t
  \]
  
- **Southern beach:**
  The cost to rent a jet ski is $8 as a base fee, plus $18 per hour.
  So, the equation for the cost $ D $ after renting for $ t $ hours is:
  \[
  D = 8 + 18t
  \]

### Part b) Completing the table for costs:
We already have partial values in the table for both beaches (up to 5 hours), but I will go through the process of filling in the missing values:

For the **Northern Beach** equation $ C = 20 + 12t $:
- When $ t = 0 $: $ C = 20 + 12(0) = 20 $
- When $ t = 1 $: $ C = 20 + 12(1) = 32 $
- When $ t = 2 $: $ C = 20 + 12(2) = 44 $
- When $ t = 3 $: $ C = 20 + 12(3) = 56 $
- When $ t = 4 $: $ C = 20 + 12(4) = 68 $
- When $ t = 5 $: $ C = 20 + 12(5) = 80 $

For the **Southern Beach** equation $ D = 8 + 18t $:
- When $ t = 0 $: $ D = 8 + 18(0) = 8 $
- When $ t = 1 $: $ D = 8 + 18(1) = 26 $
- When $ t = 2 $: $ D = 8 + 18(2) = 44 $
- When $ t = 3 $: $ D = 8 + 18(3) = 62 $
- When $ t = 4 $: $ D = 8 + 18(4) = 80 $
- When $ t = 5 $: $ D = 8 + 18(5) = 98 $

It looks like some of these values differ slightly from what's filled in on the table, but the calculated values above are based on the equations provided.

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Would you like further clarification on any part? Here are some related questions to extend your understanding:

1. How would the equations change if the hourly rates were adjusted?
2. What would the costs be after renting for 6 hours at both beaches?
3. Can you graph the cost functions for both beaches on the same axes to compare visually?
4. At what rental time do the costs of both beaches become equal?
5. How would the base cost (initial fee) affect the decision on which beach to rent from?

**Tip**: When comparing two different pricing models, it helps to look at where the costs intersect to find which option becomes more economical at different points in time.

The cost of hiring a jet-ski on northern beach is $20 plus $12 per hour, and on southern beach is $8 plus $18 per hour. The jet-skis can be rented for up to 5 hours. a) If C is the cost of renting at northern beach, D is the cost of renting at southern beach and t is the length of time the jet-skis are rented for, complete the equations below relating cost to the length of rental. b) Complete the table below for the first 5 hours (t=0-5) for both beach C and beach D.

Solve a real-world problem involving the cost of jet-ski rentals at two different beaches. Learn how to set up linear equations based on base fees and hourly rates and complete a table showing costs for the first five hours. Suitable for students in Grades 6-8.

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