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 and $y$ be the cost of a text message. We have the system of equations:
$200x + 400y=80$ (first - month usage) and $150x + 350y = 67.5$ (second - month usage).
The first equation can be simplified to $x + 2y=0.4$ (divide by 200), so $x=0.4 - 2y$.

Step2: Substitute into the second equation

Substitute $x = 0.4-2y$ into $150x + 350y=67.5$.
$150(0.4 - 2y)+350y=67.5$.
Expand: $60-300y + 350y=67.5$.
Combine like - terms: $50y=67.5 - 60=7.5$.
Solve for $y$: $y=\frac{7.5}{50}=0.15$.

Step3: Find the value of $x$

Substitute $y = 0.15$ into $x=0.4 - 2y$.
$x=0.4-2\times0.15=0.4 - 0.3 = 0.1$.

Step4: Analyze the cost differences

The cost of a text message ($y = 0.15$) and the cost of an anytime - minute ($x = 0.1$).
The difference $y - x=0.15 - 0.1=0.05$.

Answer:

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