Charlie will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $67.98 and costs an additional $0.09 per mile driven. The second plan has an initial fee of $59.98 and costs an additional $0.14 per mile driven. How many miles would Charlie need to drive for the two plans to cost the same?

Question

Charlie will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $67.98 and costs an additional $0.09 per mile driven. The second plan has an initial fee of $59.98 and costs an additional $0.14 per mile driven. How many miles would Charlie need to drive for the two plans to cost the same?

Answer 1

Let's say Charlie drives x miles.

For the first plan, the total cost would be 67.98 + 0.09 * x.
For the second plan, the total cost would be 59.98 + 0.14 * x.
To find when the two plans cost the same, we set the two expressions equal to each other: 67.98 + 0.09 * x = 59.98 + 0.14 * x.
Subtracting 0.09 * x and 59.98 from both sides, we get 67.98 - 59.98 = 0.14 * x - 0.09 * x.
Simplifying the left side gives us 8 = 0.05 * x.
Dividing both sides by 0.05 gives x = 8 / 0.05 = 160.
Therefore, Charlie would need to drive 160 miles for the two plans to cost the same. Answer: \boxed{160}.

Answer 2

Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but charges $0.18 for each minute of calls. The second plan has a $17 monthly fee and charges an additional $0.14 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 3

Let's say the minutes of calls for the two plans to cost the same is x.

For the first plan, the cost would be 0.18 * x since there's no monthly fee.
For the second plan, the cost would be $17 + 0.14 * x.
To find when the two plans cost the same, we set the two expressions equal to each other: 0.18 * x = $17 + 0.14 * x.
Subtracting 0.14 * x from both sides gives us 0.18 * x - 0.14 * x = $17.
Simplifying the left side gives us 0.04 * x = $17.
Dividing both sides by 0.04 gives x = $17 / 0.04 = 425.
Therefore, the costs of the two plans will be equal at 425 minutes of calls. Answer: \boxed{425}.

Answer 4

To find the number of miles Charlie would need to drive for the two plans to cost the same, we need to set up an equation.

Let's assume the number of miles driven is represented by "m".

For the first plan, the cost would be the initial fee plus the cost per mile driven:
Cost of first plan = $67.98 + ($0.09 * m)

For the second plan, the cost would be the initial fee plus the cost per mile driven:
Cost of second plan = $59.98 + ($0.14 * m)

Now, we can set up the equation:

$67.98 + ($0.09 * m) = $59.98 + ($0.14 * m)

To solve this equation, we can start by subtracting $59.98 from both sides:

$67.98 - $59.98 + ($0.09 * m) - ($0.14 * m) = $0.14 * m - $0.09 * m

Simplifying the equation gives:

$8 + ($0.05 * m) = $0.05 * m

Now, we can subtract $0.05 * m from both sides:

$8 = $0

Since $8 cannot be equal to $0, there is no solution to this equation.

Therefore, there is no mileage at which the two plans will cost the same.

Answer 5

To find how many miles Charlie would need to drive for the two plans to cost the same, we need to set up an equation based on the information given.

Let's assume the number of miles Charlie needs to drive is 'x'.

For the first plan, the cost can be represented as:
Cost1 = $67.98 + $0.09 * x

And for the second plan, the cost can be represented as:
Cost2 = $59.98 + $0.14 * x

We want to find the value of 'x' when the two costs are equal, so we can set up the equation:
$67.98 + $0.09 * x = $59.98 + $0.14 * x

Now, let's solve this equation to find the value of 'x'.