Question

A cell phone company A offers a plan that costs $45.99 and includes unlimited texting. Another company B offers a plan that costs $15.99 and charges $0.25 per text. For what number of texts does the second company B's plan cost more than the first company A's plan? Write an inequality that models this situation​

Answer 1

To find the break-even point for text messages between Company A and Company B's plans, an inequality is set up. The result is that Company B's plan is more expensive when more than 120 texts are sent.

Step-by-step explanation:

To determine the number of texts at which Company B's plan becomes more expensive than Company A's plan, we need to set up an inequality. Let t represent the number of text messages.

Company A's plan is a flat $45.99, which we can represent as 45.99.

Company B's plan is $15.99 plus $0.25 per text, which can be represented as 15.99 + 0.25t.

To find out when Company B's plan is more expensive than Company A's plan, our inequality is:

15.99 + 0.25t > 45.99

Subtract 15.99 from both sides to get:

0.25t > 30

Now divide both sides by 0.25 to find the number of texts:

t > 120

So Company B's plan costs more than Company A's plan when the number of text messages exceeds 120.