Question

You are choosing between two texting plans. One plan has a monthly fee of $15 with a charge of $0.05 per text. The other plan has a monthly fee of $5 with $0.07 per text. For how many text messages will the costs for the two plans be the same?

Answer 1

Answer: 500 messages will the costs for the two plans be the same.

Step-by-step explanation:

Let x= Number of text messages .

Given: One plan has a monthly fee of $15 with a charge of $0.05 per text.

i.e. Total cost of plan = 15+0.05x

The other plan has a monthly fee of $5 with $0.07 per text.

i.e. Total cost of plan = 5+0.07x

As per given ,

$5+0.07x=15+0.05x\\\\\Rightarrow\ 0.07x-0.05x=15-5\\\\\Rightarrow\ 0.02x=10\\\\\Rightarrow\ x=\dfrac{10}{0.02}\\\\\Rightarrow\ x= \dfrac{1000}{2}\\\\\Rightarrow\ x=500$

Hence, 500 messages will the costs for the two plans be the same.