Question

A cell phone company charges $50 for unlimited calls and $0.25 per text message. Another cell phone company charges $0.15 per text message and$70 for unlimited calls. How many text messages would have to be sent for the plans to cost the same amount?

Answer 1

200 text messages

Explanation:

Let x = number of text messages.

"$50 for unlimited calls and $0.25 per text message"

cost is 50 + 0.25x

"$0.15 per text message and$70 for unlimited calls"

cost is 70 + 0.15x

Set the costs equal and solve for x.

50 + 0.25x = 70 + 0.15x

Subtract 0.15x from both sides.

50 + 0.1x = 70

Subtract 50 from both sides.

0.1x = 20

Divide both sides by 0.1

x = 200

Answer: 200 text messages

Check: let x = 200

$50 for unlimited calls and $0.25 per text message"

cost is 50 + 0.25(200) = 50 + 50 = 100

The first plan costs $100 for 200 text messages.

"$0.15 per text message and$70 for unlimited calls"

cost is 70 + 0.15(200) = 70 + 30 = 100

The second plan also costs $100 for 200 text messages.

The answer 200 text messages is correct,