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 on pizza and ice cream write the equation for this situation how much does each ride cost show all your work
Let's represent the amount of money Owen and Charollet's mom gives them as "x".
The cost of each ride can be represented as "r".
The amount Owen spends on pizza can be represented as "5 dollars".
The amount Charollet spends on pizza and ice cream can be represented as "6.50 dollars".
The equation for Owen's spending can be written as: 8r + 5 = x
The equation for Charollet's spending can be written as: 5r + 6.50 = x
To find the cost of each ride, we need to solve the equation for "r" in one of the equations. Let's solve the equation for Owen's spending:
8r + 5 = x
8r = x - 5
r = (x - 5) / 8
So, the cost of each ride can be represented as (x - 5) / 8.
To determine how much each ride costs, we need an additional piece of information such as the total amount of money given by their mom or the value of "x".
Let's define some variables to represent the unknowns in this situation:
Let "x" represent the cost of each ride.
Let "m" represent the total amount of money Owen and Charollet's mom gives them.
Let "d" represent the amount Owen spends on pizza.
Let "r" represent the number of rides Owen goes on.
Let "c" represent the amount Charollet spends on both pizza and ice cream.
Let "s" represent the number of rides Charollet goes on.
Based on the given information, we can form two equations:
1) Owen goes on 8 rides and spends $5 on pizza:
r = 8 (Owen goes on 8 rides)
d = 5 (Owen spends $5 on pizza)
2) Charollet goes on 5 rides and spends $6.50 on pizza and ice cream:
s = 5 (Charollet goes on 5 rides)
c = 6.50 (Charollet spends $6.50 on pizza and ice cream)
Now we can form the equation for the total amount of money their mom gives them:
m = d + c
Since we know the values of d and c from the given information, we can substitute those values:
m = 5 + 6.50
m = 11.50
To find the cost of each ride (x), we can divide the total amount of money their mom gives them by the sum of the number of rides Owen and Charollet go on:
x = m / (r + s)
Plugging in the known values:
x = 11.50 / (8 + 5)
x = 11.50 / 13
x ≈ 0.88
So, each ride costs approximately $0.88.
To solve this problem, let's break down the information given step by step:
1. Owen goes on 8 rides and spends 5 dollars on pizza. Let's assume the cost of each ride is represented by the variable "x." Therefore, Owens spends 8x dollars on rides.
Owen's total spending = 8x + 5 dollars ... (Equation 1)
2. Charollet goes on 5 rides and spends 6.50 dollars on pizza and ice cream. Similarly, the cost of each ride is represented by the variable "x." Therefore, Charollet spends 5x dollars on rides.
Charollet's total spending = 5x + 6.50 dollars ... (Equation 2)
Since their mom gives them the same amount of money to spend at the fair, we can set the two equations equal to each other:
8x + 5 = 5x + 6.50
By solving this equation, we can find the value of "x," which represents the cost of each ride. Let's solve it step by step:
8x + 5 = 5x + 6.50
Subtract 5x from both sides of the equation:
8x - 5x + 5 = 5x - 5x + 6.50
Simplify the equation:
3x + 5 = 6.50
Subtract 5 from both sides of the equation:
3x + 5 - 5 = 6.50 - 5
Simplify the equation:
3x = 1.50
To find the value of "x," divide both sides of the equation by 3:
3x / 3 = 1.50 / 3
Simplify the equation:
x = 0.50
Therefore, each ride costs 0.50 dollars.