A ride-share service charges a fixed booking fee of \1.50 per mile traveled. Which equation gives the total cost , in dollars, of a ride that covers miles?

Solution available with step-by-step explanation

SAT Linear Functions Question 79 | Free SAT Prep | Aniko

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Question 79·Easy·Linear Functions

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A ride-share service charges a fixed booking fee of $2 and an additional $1.50 per mile traveled. Which equation gives the total cost $C$ , in dollars, of a ride that covers $m$ miles?

For linear function word problems, first separate the fixed amount (what you pay even for 0 units) from the rate per unit (what you pay for each mile, hour, etc.). Then write the equation in the form $\text{total} = (\text{rate}) \cdot (\text{units}) + (\text{fixed amount})$ . Finally, match this structure to the answer choices by checking which number multiplies the variable and which stands alone as the constant term.

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Separate fixed and changing costs

Ask yourself: what amount do you pay no matter how many miles you travel, and what amount depends on the number of miles?

Connect the changing cost to $m$

Which part of the cost should be multiplied by $m$ ? Look for the phrase that includes "per mile" in the problem.

Match constant term and coefficient

In the equation, the coefficient of $m$ should be the per-mile charge, and the constant term should be the fixed booking fee. Check each option for which number is with $m$ and which is by itself.

Desmos Guide

Compute a sample total cost from the description

In Desmos, type an expression that follows the words in the problem for a specific distance, for example for 3 miles: 2 + 1.5*3. Note the numerical result; this is the true cost for a 3-mile ride based on the description.

Test each answer choice using the same number of miles

For the same $m$ -value (for example, $m=3$ ), type each option with 3 substituted for $m$ : 2*3 + 1.5, 2*3 + 1.5*3, 1.5 + 2*3, and 1.5*3 + 2. Compare each result to the cost from Step 1; the option that matches that cost is the correct equation.

Step-by-step Explanation

Identify the two parts of the cost

The problem describes two parts of the ride cost:

A fixed booking fee of $2 (this does not depend on miles).
An additional charge of $1.50 per mile, which does depend on the number of miles $m$ .

So the total cost is:

fixed amount + (per-mile rate) × (number of miles).

Write a general equation for total cost

Let $C$ be the total cost and $m$ be the number of miles traveled.

Using the structure from Step 1:

C = (\text{per-mile rate}) \cdot m + (\text{fixed fee})

Here, the per-mile rate is $1.50 and the fixed fee is $2, but we will substitute them in the next step.

Substitute the given values into the equation

Now plug the specific values into the general form:

Per-mile rate = $1.50
Fixed fee = $2

So the equation becomes:

C = 1.50m + 2

This matches choice D, so $C = 1.50m + 2$ is the correct equation.

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Step-by-step Explanation

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Step-by-step Explanation