Final answer:
A tape diagram for Lily's taxi ride would start with a segment labeled $2.10 for the pick-up fee, and additional equal segments representing increments of $2.75 to match the total fare of $15.85. The number of these $2.75 segments corresponds to the number of miles driven, calculated by subtracting the pick-up fee from the total and dividing by the cost per mile.
Step-by-step explanation:
To determine which tape diagram could represent the context of Lily's taxi ride where m represents the number of miles, we first understand the situation mathematically. The taxi company charges a pick-up fee of $2.10 plus $2.75 per mile for the taxi ride. The total fare Lily paid, not including the tip, was $15.85. So, we're looking for a tape diagram that starts with a segment labeled $2.10 for the pick-up fee, followed by equal segments indicating multiple instances of $2.75 which add up to the remaining fare when combined with the pick-up fee.
A suitable tape diagram would therefore consist of one segment to represent the one-time pick-up fee and a series of identical segments to represent the price per mile for each mile traveled. To find out how many miles were traveled, we can set up the equation:
m = (Total fare - Pick-up fee) / Cost per mile
m = ($15.85 - $2.10) / $2.75
By solving this equation, we can determine the value of m, which will be the number of segments in the tape diagram, minus the initial pick-up fee segment.