Question

Cell phone A charges $20 per month plus $0.05 per text. Cell phone company B charges $10 per month plus $0.07 per text message. Is there any number of text messages that will result in the exact same charge from both companies?

Answer 1

The number of text messages that will result in the exact same charge from both companies is 500

Solution:

Let "x" be the number of text messages

Cell phone A charges $20 per month plus $0.05 per text

Thus, a equation for cell phone A is framed as:

Cell phone A : 20 + 0.05(number of messages)

Cell phone A : 20 + 0.05x --------- eqn 1

Cell phone company B charges $10 per month plus $0.07 per text message

Thus, a equation for cell phone B is framed as:

Cell phone B: 10 + 0.07(number of messages)

Cell phone B : 10 + 0.07x ---------- eqn 2

For exact same charge from both companies, eqn 1 must be equal to eqn 2

$20+0.05x = 10+0.07x\\\\0.07x - 0.05x = 20-10\\\\0.02x = 10\\\\Divide\ both\ sides\ of\ equation\ by\ 0.02\\\\x = 500$

Thus, the number of text messages that will result in the exact same charge from both companies is, 500