Owen and Charollet's mom gives them the same amount of money to spend at the fair they both spend all of their money Owen goes on 8 rides and spends 5 dollars on pizza while Charollet goes on 5 rides and spends 6.50 dollars on pizza and ice cream write the equation for this situation how much does each ride cost show all your work
Let's assume the amount of money their mom gave them is "m" dollars.
Owen spent 5 dollars on pizza and went on 8 rides. Let's represent the cost of each ride as "x". So the total amount Owen spent on rides is 8x. Therefore, the equation for Owen's spending is:
5 + 8x = m
Charollet spent 6.50 dollars on pizza and ice cream. Let's represent the cost of each ride as "x" (which is the same as Owen's situation). She went on 5 rides, so the equation for Charollet's spending is:
6.50 + 5x = m
To determine the cost of each ride, we can solve for "x" in either equation.
Let's solve for "x" in Owen's equation:
8x = m - 5
x = (m - 5) / 8
Therefore, the cost of each ride for Owen is (m - 5) / 8 dollars.
Now let's solve for "x" in Charollet's equation:
5x = m - 6.50
x = (m - 6.50) / 5
Therefore, the cost of each ride for Charollet is (m - 6.50) / 5 dollars.
Let's denote the amount of money given by their mom as "x".
Owen spent 5 dollars on pizza and went on 8 rides. We can represent the cost of each ride as "r".
So, the equation for Owen's spending can be written as:
5 + 8r = x
Charollet spent 6.50 dollars on pizza and ice cream and went on 5 rides. We can also represent the cost of each ride as "r".
Therefore, the equation for Charollet's spending can be written as:
6.50 + 5r = x
To find the cost of each ride (r), we need to solve the equations simultaneously.
We subtract 5 from both sides of Owen's equation and subtract 6.50 from both sides of Charollet's equation:
8r = x - 5
5r = x - 6.50
Now we have a system of two equations:
8r = x - 5
5r = x - 6.50
To solve this system, we can set the right sides of the equations equal to each other:
x - 5 = x - 6.50
By canceling out the "x" terms on both sides, we get:
-5 = -6.50
This is not true, so there is no solution to the system of equations. It is not possible to determine the cost of each ride without additional information.
To find the cost of each ride, we can start by assigning variables to the unknown quantities. Let's say the cost of each ride is represented by 'r'.
According to the given information:
Owen spent 5 dollars on pizza and went on 8 rides.
Charollet spent 6.50 dollars on pizza and ice cream and went on 5 rides.
We can write the equation for this situation as follows:
5 + 8r = 6.50 + 5r
Here's how we got the equation:
- Owen spent $5 on pizza, so we added 5 to the equation.
- Owen went on 8 rides (which cost 'r' dollars each), so we added 8r.
- Charollet spent $6.50 on pizza and ice cream, so we added 6.50 to the equation.
- Charollet went on 5 rides (which cost 'r' dollars each), so we added 5r.
Now, let's have a look at the equation we obtained:
5 + 8r = 6.50 + 5r
To find the value of 'r', we can solve this equation:
First, subtract 5r from both sides:
5 + 8r - 5r = 6.50
Simplifying:
8r - 5r = 6.50 - 5
Combine like terms:
3r = 1.50
Finally, divide both sides by 3:
r = 0.50
Therefore, each ride costs 0.50 dollars.