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: Define variables

Let $x$ = cost per anytime minute (dollars), $y$ = cost per text (dollars)

Step2: Set up system of equations

$$200x + 400y = 80$$
$$150x + 350y = 67.50$$

Step3: Simplify first equation

Divide by 200: $x + 2y = 0.40 \implies x = 0.40 - 2y$

Step4: Substitute into second equation

Substitute $x$: $150(0.40 - 2y) + 350y = 67.50$

Step5: Solve for y

$$60 - 300y + 350y = 67.50$$
$$50y = 7.50 \implies y = 0.15$$

Step6: Solve for x

Substitute $y$: $x = 0.40 - 2(0.15) = 0.10$

Step7: Compare costs

$x = 0.10$ (10 cents), $y = 0.15$ (15 cents). $y - x = 0.05$ (5 cents)

Answer:

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