A rental truck costs $50 plus $0.50 (67)
per mile.
(a) Write an equation that gives the cost C of driving
the truck x miles.
(b) Use the intersection-of-graphs method to determine
the number of miles that the truck is driven
if the rental cost is $80.
(c) Solve part (b) numerically with a table of values
(a) To write an equation that gives the cost C of driving the truck x miles, we need to consider the fixed cost (the amount that doesn't change with the number of miles driven) and the variable cost (the amount that depends on the number of miles driven).
The fixed cost in this case is $50, and the variable cost is $0.50 per mile. We can write the equation as:
C = 50 + 0.50x
(b) Using the intersection-of-graphs method, we want to find the number of miles x when the rental cost C is $80. To do this, we need to set up an equation by equating the cost equation to $80:
80 = 50 + 0.50x
Now we can solve for x:
80 - 50 = 0.50x
30 = 0.50x
To get the value of x, divide both sides of the equation by 0.50:
30 / 0.50 = x
x = 60
So, the truck is driven 60 miles if the rental cost is $80.
(c) To solve part (b) numerically with a table of values, we can choose a range of values for x and calculate the corresponding cost C using the equation C = 50 + 0.50x.
Let's create a table with different values of x and calculate the corresponding costs:
| x | C |
|-----------|-----------|
| 40 | 70 |
| 50 | 75 |
| 60 | 80 |
| 70 | 85 |
| 80 | 90 |
From the table, we can see that when the rental cost is $80, the number of miles the truck is driven is 60, which confirms our answer from part (b).