To find the cost per day and the booking fee, we can set up a system of equations based on the information provided in the table.
Let:
- \( b \) be the booking fee.
- \( c \) be the cost per day.
The cost for each number of days can be expressed using the formula: \[ \text{Cost} = b + c \times \text{Number of Days} \]
From the data given:
- For 4 days: \[ 675 = b + 4c \]
- For 5 days: \[ 800 = b + 5c \]
- For 6 days: \[ 925 = b + 6c \]
Now, we can create a system of equations:
-
\( b + 4c = 675 \) (Equation 1)
-
\( b + 5c = 800 \) (Equation 2)
-
\( b + 6c = 925 \) (Equation 3)
We can solve this by eliminating \( b \).
Subtract Equation 1 from Equation 2: \[ (b + 5c) - (b + 4c) = 800 - 675 \ c = 125 \]
Now we have \( c \).
Next, we'll use the value of \( c \) to find \( b \). We'll substitute \( c = 125 \) back into Equation 1:
\[ b + 4(125) = 675 \ b + 500 = 675 \ b = 675 - 500 \ b = 175 \]
Thus, the solutions are:
- The cost per day is \( c = 125 \) dollars.
- The booking fee is \( b = 175 \) dollars.
Final Answers:
- The cost per day is $125.
- The booking fee is $175.
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