Question 1·Easy·Linear Equations in One Variable
A ride-sharing company charges a flat pickup fee of $3.50 and $0.80 per mile driven. If the total cost of a trip was $11.30, which equation can be used to find , the number of miles driven?
For word problems that ask you to write an equation, first identify the variable (here, miles driven). Then separate the total into a fixed part (flat fee) and a variable part (rate × quantity). Write the variable part as "(rate) × (variable)" and add the fixed part if both are charges contributing to the total. Finally, set this sum equal to the given total and compare your structure to the answer choices, checking carefully which constant is multiplied by the variable and whether the terms are added or subtracted.
Hints
Fixed fee vs. per-mile charge
Which number is paid no matter how many miles you go, and which number is paid for each mile?
Which number should multiply ?
The expression that includes should represent the money paid for each mile. Ask yourself: is the per-mile rate or ?
Add or subtract the fee?
Since both the pickup fee and the mileage charge are parts of the total cost, should they be added together or should one be subtracted from the other?
Desmos Guide
Match the story to a graph
Think of as (miles) and the total cost as . From the story, when miles, the cost should already be the pickup fee, and for each additional mile the cost should increase by the per-mile amount.
Graph each option as a cost function
For each choice, rewrite it as (an expression in ). For example, choice A becomes , choice B becomes , and so on. Enter these as separate functions in Desmos.
Compare slope and intercept to the situation
Look at each graph’s y-intercept (the cost at miles) and its slope (how much increases when increases by 1). The correct equation will have a y-intercept equal to the flat fee and a slope equal to the per-mile rate ; the option whose graph has these features matches the problem.
Step-by-step Explanation
Identify what the variable represents
The problem says is the number of miles driven.
- The per-mile charge must be multiplied by .
- The flat pickup fee is a one-time amount that does not get multiplied by .
Translate each part of the cost into algebra
From the problem:
- Flat pickup fee: this is just .
- Per-mile charge: per mile driven, so this is .
- Total cost: the whole ride costs .
The total cost is the sum of the pickup fee and the mileage charge.
Write the equation for the total cost
Add the mileage cost and the flat fee, and set that equal to the total cost:
This matches answer choice C.