To establish the relationship between the total charge \( C \) and the length of time in hours \( h \), we can define the equation based on the information provided.
Let:
- \( x \) be the charge for the first hour,
- \( y \) be the charge for each additional hour.
From the information given, we can set up the following equations based on the total charges for 3 hours and 6 hours:
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For 3 hours: \[ C = x + 2y = 10.65 \quad \text{(Equation 1)} \]
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For 6 hours: \[ C = x + 5y = 15.30 \quad \text{(Equation 2)} \]
Now we can solve these two equations to find the values of \( x \) and \( y \).
Subtract Equation 1 from Equation 2 to eliminate \( x \):
\[ (x + 5y) - (x + 2y) = 15.30 - 10.65 \] \[ 3y = 4.65 \]
Solving for \( y \): \[ y = \frac{4.65}{3} = 1.55 \]
Now substitute \( y = 1.55 \) back into Equation 1 to solve for \( x \):
\[ x + 2(1.55) = 10.65 \] \[ x + 3.10 = 10.65 \] \[ x = 10.65 - 3.10 = 7.55 \]
Now we have \( x = 7.55 \) and \( y = 1.55 \).
We can write the relationship as:
- \( C = x + (h - 1)y \) for \( h \geq 1 \)
Thus, substituting the values for \( x \) and \( y \):
\[ C = 7.55 + (h - 1)(1.55) \]
Which can be rewritten to show it clearly as: \[ C = 7.55 + 1.55h - 1.55 \] \[ C = 1.55h + 6.00 \]
So, the complete equation that describes the relationship is:
\[ C = 1.55h + 6.00 \]
In this format:
- The equation is \( C = 1.55h + 6.00 \)
- Where \( C \) is in dollars and \( h \) is the number of hours parked.