Question

One monthly phone plan costs $20 for 250 minutes of talk plus 10 cents for every text message. Another monthly plan offers 250 minutes for $30 plus 5 cents for every text message. Caroline expects to talk less than 250 minutes a month but will use texting often. How many text messages will she need to send for both plans to cost the same?

a) 25
b) 125
c) 200
d) 1,000

Answer 1

Caroline needs to send 200 text messages for both the $20 plan with $0.10 per text and the $30 plan with $0.05 per text to cost the same.

Step-by-step explanation:

The student is asking to calculate how many text messages Caroline needs to send for two phone plans to cost the same. To solve this, we have to set up an equation based on the plans' pricing structures.

Plan 1: $20 + $0.10 per text
Plan 2: $30 + $0.05 per text

To find out when the two plans will cost the same, we will equalize their cost and solve for the number of texts (T):

20 + 0.10T = 30 + 0.05T

Moving the terms involving T to one side and constants to the other side, we get:

0.10T - 0.05T = 30 - 20

0.05T = 10

Divide both sides by 0.05 to find T:

T = 10 / 0.05

T = 200

So, Caroline needs to send 200 text messages for both plans to cost the same. The answer is option c) 200.