during one month of cell phone use, noah used 200 anytime minutes and 400 text messages, and paid $80.00…

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.

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.

Answer

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: $200x + 400y=80$ (divide by 200 gives $x + 2y = 0.4$) and $150x+350y = 67.5$ (divide by 50 gives $3x + 7y=1.35$). From $x + 2y=0.4$, we get $x=0.4 - 2y$.

Step2: Substitute into the second equation

Substitute $x = 0.4-2y$ into $3x + 7y = 1.35$. $3(0.4 - 2y)+7y=1.35$. Expand: $1.2-6y + 7y=1.35$. Combine like - terms: $y=1.35 - 1.2=0.15$.

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 relationship

The cost of a text message $y = 0.15$ (15 cents) and the cost of an anytime - minute $x = 0.1$ (10 cents). $y-x=0.15 - 0.1=0.05$. So each text message costs 5 cents more than each anytime minute.

Answer:

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