The weekly rental cost of a 20 foor recreational vehicle is $129.50 plus $0.15 per mile.
-Find a linear function that express the cost C as a function miles driven m.
- What is the rental cost if 860 miles are driven?
-How many miles were driven if the rental cost is $213.80?
Start by writing an equation
Total cost = (Fixed cost) + (Mileage charge)*(Number of miles)
Choose appropriate symbos for your terms such as
T = F + M N
in which case F would be $129.50 and M would be 0.15
Solve the equation for T when N = 860
Solve the equation for N when T = 213.80
To find a linear function that expresses the cost C as a function of miles driven m, we need to determine the slope and y-intercept of the equation.
The slope of the linear function is equal to the cost per mile, which in this case is $0.15.
The y-intercept is the fixed cost or the cost when no miles are driven, which is $129.50.
Therefore, the linear function that expresses the cost C as a function of miles driven m is:
C(m) = 0.15m + 129.50
To find the rental cost if 860 miles are driven, we can substitute m = 860 into the function:
C(860) = 0.15(860) + 129.50
C(860) = 129 + 258 + 129.50
C(860) = $387.50
The rental cost if 860 miles are driven is $387.50.
To find out how many miles were driven if the rental cost is $213.80, we can rearrange the function as:
213.80 = 0.15m + 129.50
Subtract 129.50 from both sides:
213.80 - 129.50 = 0.15m
84.30 = 0.15m
Divide both sides by 0.15:
84.30 / 0.15 = m
562 = m
So, if the rental cost is $213.80, then 562 miles were driven.
To find the linear function that expresses the cost C as a function of miles driven m, we need to determine the equation in the form of y = mx + b, where y represents the cost, m represents the cost per mile, x represents the number of miles driven, and b represents the fixed cost.
Given that the fixed cost is $129.50 and the cost per mile is $0.15, we can substitute these values into the equation:
C = 0.15m + 129.50
To find the rental cost if 860 miles are driven, we substitute the value of m = 860 into the equation and solve for C:
C = 0.15 * 860 + 129.50
C = 129 + 129.50
C = $258.50
Therefore, the rental cost if 860 miles are driven is $258.50.
To determine how many miles were driven if the rental cost is $213.80, we set up the equation and rearrange it to solve for m:
213.80 = 0.15m + 129.50
84.30 = 0.15m
By isolating m, we divide both sides of the equation by 0.15:
m = 84.30 / 0.15
m = 562
Therefore, the number of miles driven if the rental cost is $213.80 is 562 miles.