To find the cost of a full tank of gas, we first need to determine the price per hour for the boat rental. We can do this by calculating the difference in rental fees for different hours.
Let's look at the rental fees:
- For 2 hours: $83
- For 4 hours: $135
- For 6 hours: $187
- For 8 hours: $239
Now, let's calculate the rental fees for each additional hour:
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From 2 hours to 4 hours: \[ 135 - 83 = 52 \] The cost for 2 additional hours is $52, so the hourly rate is: \[ \frac{52}{2} = 26 \]
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From 4 hours to 6 hours: \[ 187 - 135 = 52 \] Again, the cost for 2 additional hours is $52.
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From 6 hours to 8 hours: \[ 239 - 187 = 52 \] The cost for 2 additional hours is still $52.
This confirms that the hourly rental fee is $26.
Now we can calculate the total cost that includes the rental fee plus the cost of a full tank of gas. Let \( C \) be the cost of the full tank of gas.
Using the rental fee equations:
- For 2 hours: \[ 2(26) + C = 83 \] \[ 52 + C = 83 \] \[ C = 83 - 52 = 31 \]
We can verify this calculation with the other rental periods.
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For 4 hours: \[ 4(26) + C = 135 \] \[ 104 + C = 135 \] \[ C = 135 - 104 = 31 \]
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For 6 hours: \[ 6(26) + C = 187 \] \[ 156 + C = 187 \] \[ C = 187 - 156 = 31 \]
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For 8 hours: \[ 8(26) + C = 239 \] \[ 208 + C = 239 \] \[ C = 239 - 208 = 31 \]
Thus, we consistently find that the cost of a full tank of gas is $31.
The answer is: D. $31
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