Question

during one month of cell phone use, noah used 200 anytime minutes and 400 text messages, and paid $80.00. the next month, he used 150 anytime minutes and 350 text messages, and paid $67.50. which statement is true? each text message costs 5 cents more than each anytime minute. each anytime minute costs 10 cents more than each text message. a text message and an anytime minute each cost 25 cents. each text message costs double the amount of an anytime minute.

Explanation:

Step1: Set up equations

Let \(x\) be the cost of an anytime - minute (in dollars) and \(y\) be the cost of a text - message (in dollars).
For the first month: \(200x + 400y=80\), which simplifies to \(x + 2y = 0.4\) (divide by 200).
For the second month: \(150x+350y = 67.5\), which simplifies to \(3x + 7y=1.35\) (divide by 50).
From \(x + 2y=0.4\), we get \(x=0.4 - 2y\).

Step2: Substitute \(x\) into the second equation

Substitute \(x = 0.4-2y\) into \(3x + 7y=1.35\).

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Step3: Find \(x\)

Substitute \(y = 0.15\) into \(x=0.4 - 2y\).

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\(x = 0.1\) dollars (10 cents) and \(y = 0.15\) dollars (15 cents).

Answer:

Each text message costs 5 cents more than each anytime minute.