A ride-sharing company charges a fixed booking fee of dollars per trip plus dollars per mile. For a 22-mile trip, the total cost was \$15.80. What was the booking fee for this trip?

Solution available with step-by-step explanation

SAT Linear Equations in One Variable Question 5 | Free SAT Prep | Aniko

00:00

Question 5·Medium·Linear Equations in One Variable

0 / 140

A ride-sharing company charges a fixed booking fee of $b$ dollars per trip plus $0.40$ dollars per mile. For a 22-mile trip, the total cost was $15.80.

What was the booking fee for this trip?

For linear cost problems with a fixed fee plus a per-unit charge, always start by defining a variable for the fixed fee and writing an equation: total cost = fixed fee + (rate × quantity). Substitute the given numbers, simplify the variable part (here, multiply the per-mile rate by the number of miles), then isolate the unknown with one inverse operation (usually subtraction). Keeping the equation organized and doing each arithmetic step carefully helps avoid small decimal mistakes and lets you answer quickly and confidently on the SAT.

Hints

Click me!

Identify fixed vs. variable parts

Separate the charge that stays the same every trip (the booking fee) from the charge that depends on the number of miles (the $0.40$ per mile). How can you write the total cost using these two parts?

Write and simplify the equation

For a $22$ -mile trip, what is the expression for the mileage cost using $0.40$ dollars per mile? Plug this into an equation where total cost equals booking fee plus mileage cost.

Solve for the unknown

Once you have an equation like $b + \text{(mileage cost)} = 15.80$ , what operation should you use to get $b$ by itself?

Desmos Guide

Calculate the booking fee directly

In a new expression line, type 15.8 - 0.40*22 to represent total cost minus mileage cost. The numerical result that Desmos displays is the booking fee for the trip.

Step-by-step Explanation

Translate the situation into an equation

The total cost of the trip equals the fixed booking fee plus the cost per mile.

Let the booking fee be $b$ dollars.

For a $22$ -mile trip, the cost per mile is $0.40$ dollars, so the mileage cost is $0.40 \times 22$ .

So the equation for the total cost is:

b + 0.40 \times 22 = 15.80

Find the total mileage cost

Calculate the cost for the $22$ miles:

0.40 \times 22 = 8.8

Now substitute that back into the equation:

b + 8.8 = 15.8

Isolate the booking fee

To solve for $b$ , subtract the mileage cost $8.8$ from both sides of the equation:

b + 8.8 - 8.8 = 15.8 - 8.8

This simplifies to:

b = 15.8 - 8.8

Compute the booking fee and match the answer choice

Now do the subtraction:

15.8 - 8.8 = 7

So the booking fee is $b = 7$ dollars, which is $7.00$ .

The correct answer is $7.00$ (Choice C).

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation