Solve the problem.A taxi company charges riders a fixed charge of $2.30 plus $1.20 per mile. How many miles must a rider go to have an average cost per mile of $1.30?
total cost=2.30+1.2m
1.30m=2.30+1.2m
.10m=2.3
m=23 miles
check that
To solve this problem, we need to find out the number of miles a rider must go to have an average cost per mile of $1.30.
Let's break down the information we have:
- Fixed charge: $2.30
- Cost per mile: $1.20
- Desired average cost per mile: $1.30
We can set up an equation to represent this problem:
Total cost = Fixed charge + (Cost per mile * Number of miles)
Let's use x to represent the number of miles the rider must go.
Therefore, the equation becomes:
Total cost = $2.30 + ($1.20 * x)
Since we want the average cost per mile to be $1.30, we can write another equation:
Average cost = Total cost / Number of miles
Plugging in the values we have:
$1.30 = ($2.30 + ($1.20 * x)) / x
To solve for x, we can multiply both sides of the equation by x:
$1.30 * x = $2.30 + ($1.20 * x)
Now, we can solve for x by isolating it on one side of the equation. Let's subtract ($1.20 * x) from both sides:
$1.30 * x - $1.20 * x = $2.30
Applying the calculation:
$0.10 * x = $2.30
Dividing both sides by $0.10:
x = $2.30 / $0.10
Performing the division:
x = 23
Thus, the rider must go 23 miles to have an average cost per mile of $1.30.