To determine which situation is represented by the given table, we can use the general formula for the total cost \( y \) in relation to the distance traveled \( x \):
\[ y = \text{base fee} + (\text{charge per mile} \times x) \]
We'll consider each option and see which one fits the data provided in the table.
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Option A: Base fee = $7, Charge per mile = $1.65 \[ y = 7 + 1.65x \]
- For \( x = 5 \): \( y = 7 + 1.65(5) = 7 + 8.25 = 15.25 \) (not $14.25)
- This option does not fit.
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Option B: Base fee = $5, Charge per mile = $9.25 \[ y = 5 + 9.25x \]
- For \( x = 5 \): \( y = 5 + 9.25(5) = 5 + 46.25 = 51.25 \) (not $14.25)
- This option does not fit.
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Option C: Base fee = $10, Charge per mile = $4.25 \[ y = 10 + 4.25x \]
- For \( x = 5 \): \( y = 10 + 4.25(5) = 10 + 21.25 = 31.25 \) (not $14.25)
- This option does not fit.
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Option D: Base fee = $5, Charge per mile = $1.85 \[ y = 5 + 1.85x \]
- For \( x = 5 \): \( y = 5 + 1.85(5) = 5 + 9.25 = 14.25 \) (matches)
- For \( x = 10 \): \( y = 5 + 1.85(10) = 5 + 18.5 = 23.50 \) (matches)
- For \( x = 15 \): \( y = 5 + 1.85(15) = 5 + 27.75 = 32.75 \) (matches)
- For \( x = 20 \): \( y = 5 + 1.85(20) = 5 + 37 = 42 \) (matches)
Since Option D matches all entries in the provided table, the correct answer is:
D. The base fee for hiring a cab is $5, and there is an additional charge of $1.85 per mile.
1 answer