Question

A taxi charges a flat rate of $3.00, plus an additional

$0.50 per mile. Carl will only take the taxi home if the
cost is under $10, otherwise he will take a bus. Carl is 15
miles from home. Explain how to write and solve an
inequality to determine if Carl will take the taxi or a bus.

Answer 1

The taxi fare is the total of two expenses:

the $3.00 flat fee and the $0.50 per mile surcharge

Let x represent the amount of miles.

The mile cost is 0.5x for x miles.

$3.00 + 0.5x is the total cost.

0.5x + 3 = total cost

The entire cost must be less than $10, thus the sum of the two expenses must be less than that.

The disparity is as follows:

0.5x + 3 x x x x x x x x x

Subtract 3 from both sides of the equation.

0.5x

Subtract 0.5 from both sides.

14 × 14

If the trip is less than 14 miles, the fee is less than $10.

Because the trip is 15 miles, a cab would cost more than $10, therefore Carl will take the bus.

Explanation:

Answer 2

cost = 3 + 0.5m

Carl will take a bus.

Explanation:

cost = fixed fee + mileage rate

Let m = number of miles.

cost = 3 + 0.5m

For 15 miles, m = 15.

cost = 3 + 0.5 × 15

cost = 3 + 7.5

cost = 10.5

For 15 miles, the cost is $10.50.

Carl will take a bus.