Answer: you need to send 300 text messages for the cost to be the same.
Step-by-step explanation:
Let x represent the number of text messages that you have to send for the cost of using either plans to be the same.
For the first plan, you can get 500 free text messages with a charge of $0.10 for each text message over 500. It means that the cost of sending x text messages would be
0.1(x - 500)
For the second plan, you can get 400 free text messages with a charge of $0.20 for each text message over 400. It means that the cost of sending x text messages would be
0.2(x - 400)
For the cost to be the same, the number if text messages would be
0.2(x - 400) = 0.1(x - 500)
0.2x - 80 = 0.1x - 50
0.2x - 0.1x = - 50 + 80
0.1x = 30
x = 30/0.1
x = 300
