Solution 3c. What is unknown? The number of miles the truck is driven is unknown. Let m represent the miles driven. What is known? The total cost of renting the truck is $44.95 plus $0.45 per mile and the total budgeted is $300. To find the cost of renting the truck, we calculate the cost of renting the truck for a specific number of miles and use this to determine an expression for the cost of driving the truck m miles. Number of Miles Cost of Renting 100 44.95 + 0.45(100) = $ 89.95 250 44.95 + 0.45(250) = 157.45 400 44.95 + 0.45(400) = 224.95 m 44.95 + 0.45m The equation comes from setting the cost of renting equal to the amount budgeted, $300. 44.95 + 0.45x = 300 Solving the equation enables us to determine how many miles the truck can be driven. 44.95 + 0.45x = 300 44.95 + 0.45x - 44.95 = 300 - 44.95 Subtract 44.95 from each side. 0.45x = 255.05 Simplify. 0.45x 0.45 = 255.05 0.45 Divide each side by 0.45. x = 566.78 Simplify. So, the family can drive approximately 567 miles for a cost of $300. Student Check 3 Write an equation that represents each situation. Solve the equation and explain the answer using a complete sentence. a. Four more than three times a number is -5. Find the number. b. How many nickels does it take to make $30? c. The cost to rent a car for one day is $13.99 plus $0.20 per mile. How many miles can be driven for $50? Round to the nearest mile. Consecutive Integer Problems Consecutive means “successive” or “following one after another without interruption.” So, consecutive integers are integers that follow one another. Some examples are listed in the table. Specific Example Variable Representation Consecutive integers 4 5 6 +1 +1 x, x + 1, x + 2, . . . Consecutive even integers 10 12 14 +2 +2 x, x + 2, x + 4, . . . Consecutive odd integers 11 13 15 +2 +2 x, x + 2, x + 4, . . . Objective 4 ▶ Solve consecutive integer problems. The cost of renting the truck is the flat fee of $44.95 plus a mileage fee. We multiply the miles driven by $0.45 and add this to the flat fee. 118 Chapter 2 Linear Equations and Inequalities in One Variable
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