Final answer:
Option B) y = 2x + 5; $15 is the correct equation for the cost of renting a kayak. The difference in cost between the company that charges the most and the one that charges the least for 4 hours is $32.
Step-by-step explanation:
The correct answer is option B) y = 2x + 5; $15.
To write the equation for each boat rental company, we need to determine the relationship between the cost of renting a kayak (y) and the number of hours (x) rented. From the given options, option B) y = 2x + 5; $15 represents a linear equation that expresses this relationship. In this equation, the slope is 2, which means for every additional hour rented, the cost increases by $2. The y-intercept is 5, which represents the initial cost of renting a kayak, independent of the number of hours. The cost given for 4 hours is $15.
To find the difference in cost between the company that charges the most and the one that charges the least for 4 hours, we need to compare the y-values for the different equations at x = 4. Using option B) y = 2x + 5; $15, the cost for 4 hours is 2(4) + 5 = 13.
The cost for options A) 4x - 20y = 80; $45, C) 3x + 2y = 18; $20, and D) y = 8 - 2x; $35 can be found by substituting x = 4 into the equations and solving for y.
Comparing the costs, the company that charges the most has a cost of $45, and the one that charges the least has a cost of $13 for 4 hours. Therefore, the difference in cost is $45 - $13 = $32.