Question

Explaining How to Solve a Problem
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

Let m = the number of miles Carl travels. The taxi cost C (in dollars) is
C = 3 + 0.50m.

Carl will take the taxi only if the cost is under $10, so write the inequality
3 + 0.50m < 10.

Solve it:
0.50m < 10 − 3
0.50m < 7
m < 7 / 0.50
m < 14.

So Carl will take the taxi only if the trip is less than 14 miles. For 15 miles the taxi would cost
3 + 0.50(15) = 3 + 7.50 = $10.50,
which is more than $10, so Carl will take the bus. (If the trip were exactly 14 miles the cost would be $10; since he requires "under $10," he would still take the bus.)