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.

See below.

Step-by-step explanation:

The cost of the taxi is the sum of two costs:

the fixed fee of $3.00 and the $0.50 per mile.

Let x = number of miles.

For x miles, the mile cost is 0.5x

The total cost is $3.00 plus 0.5x

Total cost: 0.5x + 3

We want the total cost to be under $10, so the sum of the two costs must be less than 10.

The inequality is:

0.5x + 3 < 10

Subtract 3 from both sides.

0.5x < 7

Divide both sides by 0.5

x < 14

The cost is under $10 if the distance is under 14 miles.

Since the distance here is 15 miles, the cost of the taxi is over $10, and Carl will take the bus.