Question

analyzing a solution to a system of equations
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 cents) and $y$ be the cost of a text message (in cents).
The first - month situation gives the equation $200x + 400y=8000$ (since $80$ dollars = $8000$ cents). Simplify it to $x + 2y=40$ (divide by 200), so $x=40 - 2y$.
The second - month situation gives the equation $150x+350y = 6750$ (since $67.5$ dollars = $6750$ cents). Simplify it to $3x + 7y=135$ (divide by 50).

Step2: Substitute $x$ into the second equation

Substitute $x = 40-2y$ into $3x + 7y=135$.
$3(40 - 2y)+7y=135$.
Expand: $120-6y + 7y=135$.
Combine like - terms: $y=135 - 120=15$.

Step3: Find the value of $x$

Substitute $y = 15$ into $x=40 - 2y$.
$x=40-2\times15=40 - 30 = 10$.

Step4: Analyze the cost relationship

The cost of an anytime - minute $x = 10$ cents and the cost of a text message $y = 15$ cents.
So each text message costs 5 cents more than each anytime minute.

Answer:

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