Solving a Word Problem By: Jordan Williams

Word Problem A car rental company charges $24.95 per day plus $.10 per mile. A business traveler is allotted $50.00 each day for travel expenses. What is the greatest number of miles the business person can travel without going over the allotted $50.00?

Key Words greatest number of miles $.10 per mile $24.95 per day plus

Variable Chosen The variable I chose is m for miles

Inequality Symbol less than or equal because the traveler cannot go over his $50 but can spend $50 exactly

Set-Up The set-up to this equation is 24.95 + .1m ≤ 50 In one day the traveler has $50 to spend which he cannot exceed but the car cost $24.95 per day and $.10 per mile so 24.95 plus .1m needs to be under the amount of money the traveler is allowed for that day of travel.

Step 1 Subtract 24.95 from both sides 24.95 + .1m - 24.95 ≤ 50 - 24.95 Because of the subtraction property of inequality Results in .1m ≤ 25.05

Step 2 Divide both sides by .1 .1m/.1 ≤ 25.05/.1 Because of the division property of inequality Results in m ≤ 250.5

Solution m ≤ 250.5

Check m = 200, 24.95 + .1(200) = 24.95 + 20 = 44.95 which is less than 50 m = 225, 24.95 + .1(225) = 24.95 + 22.5 = 47.45 which is less than 50 m = 250.5, 24.95 + .1(250.5) = 24.95 + 25.05 = 50 which is equal to 50 but is still a solution

Answer The traveler can travel 250.5 miles without going over the allotted $50

How to Graph the Solution Closed dot at 250.5 because there is a less than or equal sign Arrow pointing left because values need to be less than 250.5 or the traveler will exceed his allotted money for the day