To determine how many signs will be posted along the 16-mile trail with a sign every 1/8 mile (including one at the end), we can follow these steps:
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Convert the total distance into eighths of a mile: \[ 16 \text{ miles} = 16 \times 8 = 128 \text{ eighths of a mile} \]
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Count the signs: Since there will be one sign at each 1/8 mile increment and one sign at the end (16 miles), the number of signs will be equal to the number of intervals between the signs plus the sign at the end.
- The first sign at 1/8 mile through to the last sign at 16 miles will include the start of each 1/8 mile up to 128.
- Therefore, we will have 128 individual increments, which means there are 128 signs total.
Thus, the answer is c) 128.