Final answer:
To find the hourly cost of renting a bike, two linear equations were set up based on the information given and then simplified to express the bike rental cost in terms of the other variables.
Step-by-step explanation:
To determine the hourly cost of renting a bike, we can set up a system of linear equations based on the information given:
- For the first tourist: 3B + 4H = $130
- For the second tourist: 8B + 2H = $208
Where B represents the cost of renting a bike per hour, and H represents the cost of horseback riding per hour. By solving this system of equations, we can find the value of B.
Firstly, we can multiply the entire first equation by 2, resulting in:
Now, we can subtract the second equation from this result to eliminate H:
- (6B + 8H) - (8B + 2H) = $260 - $208
Which simplifies to:
- 6B + 8H - 8B - 2H = $52
- -2B + 6H - 2H = $52
- -2B + 4H = $52
We are just left with B on one side.
By solving for B now:
But since we do not have the hourly rate for horseback riding, we cannot solve it directly. Instead, let's go back and isolate B in one of the original equations. We choose the first for simplicity:
- 3B = $130 - 4H
- B = ($130 - 4H) / 3
With the second equation, we do the same:
- 8B = $208 - 2H
- B = ($208 - 2H) / 8
These two expressions for B are equal to each other because they represent the same quantity, the cost of bike renting per hour. Now we need to solve this system, which might involve substituting one equation into the other and solving for one variable first or using another method such as elimination or matrix operations.