I have no clue on how to set up this equation please help.
A car rental company offers two plans for renting a car.
Plan A:21 dollars per day and 18 cents per mile
Plan B:25.44 dollars per day and 15 cents per mile
If you plan to rent the car for one day. and "m" represents the number of miles driven in that day,for how many miles driven would you save money with plan A?
m <> <= >=?
Very simple.
When is
21 + .18m = 24.44 + .15 m ?
or
2100 + 18m = 2444 + 15m
just solve for m
at the value of m, they are equal, so you decide for miles above or below that value.
thank you
To determine how many miles driven would save money with plan A, let's set up an equation to compare the costs of the two plans.
First, let's determine the cost for each plan.
For plan A, the cost would be:
Cost_A = 21 dollars + 0.18 dollars/mile * m miles
For plan B, the cost would be:
Cost_B = 25.44 dollars + 0.15 dollars/mile * m miles
To find the break-even point, we need to set the costs equal to each other and solve for 'm':
Cost_A = Cost_B
21 + 0.18m = 25.44 + 0.15m
Now, we can solve for 'm':
0.18m - 0.15m = 25.44 - 21
0.03m = 4.44
Divide both sides of the equation by 0.03 to solve for 'm':
m = 4.44 / 0.03
m ≈ 148
Therefore, for any distance less than 148 miles, you would save money with plan A. For distances greater than or equal to 148 miles, you would save money with plan B.
To determine the number of miles driven at which you would save money with Plan A, we need to compare the total cost of each plan for a given number of miles.
Let's break down the cost of each plan first:
Plan A:
- Cost per day: $21
- Cost per mile: $0.18 (18 cents)
- Total cost for Plan A: $21 + $0.18 * m (where 'm' represents the number of miles driven)
Plan B:
- Cost per day: $25.44
- Cost per mile: $0.15 (15 cents)
- Total cost for Plan B: $25.44 + $0.15 * m
To find at which number of miles driven you would save money with Plan A, we need to set up an equation to compare the two plans:
$21 + $0.18 * m < $25.44 + $0.15 * m
Now, let's solve this equation to find the value of 'm':
$21 + $0.18 * m < $25.44 + $0.15 * m
Let's isolate the 'm' term on one side by subtracting $0.15 * m from both sides:
$21 + $0.03 * m < $25.44
Next, let's subtract $21 from both sides:
$0.03 * m < $25.44 - $21
$0.03 * m < $4.44
To isolate 'm', divide both sides by $0.03:
m < $4.44 / $0.03
m < 148
Therefore, you would save money with Plan A for any number of miles driven less than 148 miles.