A phone plan costs 35 per month, which includes 200 text... | SAT Linear equations in one variable Question, Answer Explained

Question bank / Linear equations in one variable

Math · AlgebraMedium

A phone plan costs $\$35$ per month, which includes $200$ text messages. Each text message beyond the first $200$ costs $\$0.10$ , and there are no other charges. One month, Dev's bill was $\$51.40$ . How many text messages did Dev send that month?

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Answer: 364

Let $t$ be the number of text messages. Dev paid for $t - 200$ extra messages, so $35 + 0.10(t - 200) = 51.40$ . Then $0.10(t - 200) = 16.40$ , so $t - 200 = 164$ and $t = 364$ .

Stopping at $164$ gives only the messages beyond the first $200$ , not the total number Dev sent.

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