How would you solve this word problem in one variable inequality form?

One cell phone company offers a plan that costs $29.99 and includes unlimited night and weekend minutes. Another company offers a plan that costs $19.99 and charges 35 cents per minute during nights weekends. For what numbers of night and weekend minutes does the second company's plan cost more than the first company's plan?

plan1 = 29.99

plan2 =19.99 + .35m

plan2 > plan1
19.99 + .35m > 29.99
.35m > 29.99-19.99
.35m > 10
m > 10/.35
m > 28.6 minutes

it will cost more if you exceed 28 minutes

By how much does +5 exceed -5?

To determine the number of night and weekend minutes for which the second company's plan costs more than the first company's plan, we will set up an inequality.

Let's denote the number of night and weekend minutes as "x".

The total cost for the first company's plan would be a constant $29.99, regardless of the number of minutes used.

For the second company's plan, the cost will consist of the fixed monthly charge of $19.99 plus the additional cost for the minutes used during nights and weekends. Since they charge 35 cents per minute, the additional cost for x minutes would be 0.35x.

Therefore, the inequality representing the situation is:

19.99 + 0.35x > 29.99

To solve this inequality, we can begin by subtracting 19.99 from both sides:

0.35x > 29.99 - 19.99

Simplifying, we have:

0.35x > 10

Next, we divide both sides of the inequality by 0.35:

x > 10 / 0.35

Performing the division:

x > 28.5714

Therefore, the solution to the inequality is x > 28.5714.

In practical terms, for the second company's plan to cost more than the first company's plan, you would need to use more than 28.5714 night and weekend minutes.

To solve this word problem in one variable inequality form, we need to compare the costs of the two plans and find the range of numbers of night and weekend minutes where the second company's plan costs more than the first company's plan.

Let's assume the number of night and weekend minutes is represented by the variable "x".

First, let's consider the cost of the first company's plan. It is a fixed cost of $29.99, regardless of the number of night and weekend minutes. Therefore, we can represent the cost of the first company's plan as a constant: C1 = $29.99.

Next, let's consider the cost of the second company's plan. It has a base cost of $19.99 and charges an additional 35 cents per minute during nights and weekends. So, the cost of the second company's plan can be represented as: C2 = $19.99 + 0.35x, where x represents the number of night and weekend minutes.

To find the range of x where the second company's plan costs more than the first company's plan, we set up the inequality:

C2 > C1

$19.99 + 0.35x > $29.99

To solve this inequality, we can subtract $19.99 from both sides:

0.35x > $29.99 - $19.99

0.35x > $10.00

Finally, divide both sides of the inequality by 0.35:

x > $10.00 / 0.35

x > 28.57

Therefore, for any number of night and weekend minutes greater than 28.57, the second company's plan will cost more than the first company's plan.