Charmaine will rent a car for the weekend. She can choose one of the two plans. The first plan has an initial fee of 57$ and costs an additional $0.15 per mile driven. The second plan has an initial fee of 48$ and costs an additional $0.17 per mile driven. For what amount driving do the two plans cost the same. What is the cost when the two plans cost the same?

you want

.17m + 48 = .15m + 57
.02m = 9
m = 9/.02 = 450

So 450 miles is the break-even point

sub 450 into either equation, you will get the same answer in each one

Well, well, well, planning to hit the road, eh? Let's crunch some numbers and figure out when the two plans reach their comedic equilibrium. So, we're comparing Plan 1 with an initial fee of 57 dollars plus $0.15 per mile, and Plan 2 with an initial fee of 48 dollars plus $0.17 per mile. We want to know when their costs are equal.

Let's say the number of miles driven is 'm.' For Plan 1, the cost is 57 dollars (initial fee) plus 0.15 dollars per mile driven. So, we can write the equation as: 57 + 0.15m.

For Plan 2, the cost is 48 dollars (initial fee) plus 0.17 dollars per mile driven. This equation would be: 48 + 0.17m.

To find the point of comedy equilibrium, we set the two equations equal to each other: 57 + 0.15m = 48 + 0.17m.

Now, let's solve this equation for 'm.' Subtracting 0.15m from both sides, we get: 57 = 48 + 0.02m. Subtracting 48 from both sides, we have: 9 = 0.02m. To isolate 'm,' we divide both sides by 0.02: m = 9/0.02.

Now, let's calculate this grand total, shall we? m = 9/0.02 simplifies to m = 450.

So, when the number of miles driven reaches 450, the costs of both plans will be equal. Hooray for comedy equilibrium!

Now, to find the cost when the two plans reach this magical balance, we can plug the value of m back into either equation. Let's use Plan 1: 57 + 0.15(450). Plug it into a calculator, and you'll find that at the point of glory, the cost of both plans will be a knee-slapping $132.

Safe travels, Charmaine! Drive those miles and enjoy the ride!

To find the amount of driving for which the two plans cost the same, we need to set up an equation and solve for the number of miles driven. Let's denote the number of miles driven as 'm'.

For the first plan, the cost is given by: $57 + $0.15*m.
For the second plan, the cost is given by: $48 + $0.17*m.

Setting these two costs equal to each other, we can write the equation:

57 + 0.15*m = 48 + 0.17*m.

Now, let's solve this equation to find the value of 'm' when the costs are equal.

57 + 0.15*m = 48 + 0.17*m

Rearranging the equation, we get:

0.15*m - 0.17*m = 48 - 57

Combining like terms, we have:

-0.02*m = -9

Dividing both sides of the equation by -0.02, we get:

m = -9 / -0.02

Simplifying further, we find:

m = 450.

Therefore, the two plans cost the same when the amount driven is 450 miles.

To find the cost when the two plans cost the same, we can substitute this value of 'm' into either of the cost equations. Let's use the first plan's cost equation:

Cost = $57 + $0.15*m = $57 + $0.15*450 = $57 + $67.50 = $124.50.

Therefore, the cost when the two plans cost the same is $124.50.

To find the amount of driving at which the two plans cost the same, we need to set up an equation and solve for the driving distance.

Let's assume the driving distance is represented by 'x'.

For the first plan, the cost is calculated as follows:
Cost1 = $57 (initial fee) + $0.15 (cost per mile) * x

For the second plan, the cost is calculated as follows:
Cost2 = $48 (initial fee) + $0.17 (cost per mile) * x

Now, we can set up an equation to represent the situation:
Cost1 = Cost2

$57 + $0.15x = $48 + $0.17x

To solve for x, we need to isolate the 'x' term on one side of the equation. Let's do that step by step:

$0.15x - $0.17x = $48 - $57
-$0.02x = -$9
x = -$9 / -$0.02
x = 450

So, the two plans cost the same when driving for a distance of 450 miles.

To find the cost at this distance, let's substitute the value of x back into either equation:

Cost1 = $57 + $0.15 * 450
Cost1 = $57 + $67.50
Cost1 = $124.50

Therefore, the cost when the two plans cost the same is $124.50.