Answer
$More$ $than$ $300$ texts must be sent for plan A to be a better deal.
Work Step by Step
To solve this exercise, we must first model the monthly cost of each texting plan as follows: $$A_{cost} = 15 + 0.08T$$ $$B_{cost} = 3 + 0.12T$$ where $T$ represents the amount of texts one sends in a month. The exercise asks how many texts must be sent for plan A to be a better deal. In other words, when plan A is less than plan B: $$B_{cost} \gt A_{cost}$$ $$3 + 0.12T \gt 15 + 0.08T$$ By solving for T: $$0.12T- 0.08T \gt 15 - 3$$ $$0.04T \gt 12$$ $$T\gt 300$$ Which means that one must send out more than 300 texts for plan A to start being a better deal than Plan B.
