A ride-sharing service charges a flat booking fee of \0.75 per mile. Mason’s credit card was charged \$17.50 for a ride. How many miles did Mason travel?

Solution available with step-by-step explanation

SAT Linear Equations in One Variable Question 2 | Free SAT Prep | Aniko

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Question 2·Medium·Linear Equations in One Variable

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A ride-sharing service charges a flat booking fee of $2.50 plus $0.75 per mile. Mason’s credit card was charged $17.50 for a ride. How many miles did Mason travel?

Your answer

(Express the answer as an integer)

For linear cost problems with a flat fee plus a per-unit charge, always write an equation in the form total cost = flat fee + (rate × quantity). Assign a variable to the unknown quantity (here, miles), plug in the known numbers, then solve the one-step-at-a-time: subtract the flat fee from both sides, and divide by the per-unit rate. Finally, do a quick check by substituting your result back into the original cost expression to confirm it matches the given total.

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Set up the relationship

Ask yourself: What is being charged at a flat rate, and what is being charged per mile? Write an expression that combines both to equal the total cost.

Use a variable for miles

Let a variable (like $m$ ) represent the number of miles. How would you write the total ride cost using $2.50$ , $0.75$ , and $m$ ?

Undo the operations step by step

After you have the equation, first remove the flat fee by using the opposite operation. Then, to isolate the variable, use the opposite of multiplying by $0.75$ .

Check your result

Once you find a value for the miles, plug it back into the cost expression to see if it reproduces the total charge of 17.50.

Desmos Guide

Use Desmos to compute the miles directly

In Desmos, type the expression (17.5 - 2.5) / 0.75 and press Enter. The output value is the number of miles Mason traveled.

Step-by-step Explanation

Define the variable and write the equation

Let $m$ be the number of miles Mason traveled.

The ride cost is a flat fee plus a per-mile charge, so the total cost is:

2.50 + 0.75m = 17.50

This equation says: booking fee $2.50$ plus $0.75$ times $m$ miles equals the total charge $17.50$ .

Isolate the miles term

Subtract the flat booking fee $2.50$ from both sides to get the cost of just the miles:

0.75m = 17.50 - 2.50 = 15.00

Now $0.75m$ represents the cost for the miles alone.

Solve for the number of miles

To find $m$ , divide both sides of the equation by $0.75$ :

m = \frac{15}{0.75}

Notice that $0.75 = \tfrac{3}{4}$ , so dividing by $0.75$ is the same as multiplying by $\tfrac{4}{3}$ :

m = 15 \times \frac{4}{3} = 5 \times 4 = 20

So Mason traveled 20 miles.

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation