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
double the
amount of an
anytime minute.
a text message
and an anytime
minute each cost
25 cents.
each anytime
minute costs 10
cents more than
each text
message.
each text
message costs 5
cents more than
each anytime
minute.

Explanation:

Step1: Set up equations

Let \(x\) be the cost per anytime minute (in dollars) and \(y\) be the cost per text message (in dollars).
We have the system of equations:
\(200x + 400y=80\) (divide by 200: \(x + 2y = 0.4\))
\(150x+350y = 67.5\) (divide by 50: \(3x+7y=1.35\))
From \(x + 2y=0.4\), we get \(x=0.4 - 2y\)

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

Substitute \(x = 0.4-2y\) into \(3x + 7y=1.35\)
\(3(0.4-2y)+7y=1.35\)
\(1.2-6y + 7y=1.35\)
\(y=1.35 - 1.2\)
\(y = 0.15\) (15 cents)

Step3: Find \(x\)

Substitute \(y = 0.15\) into \(x=0.4-2y\)
\(x=0.4-2\times0.15\)
\(x=0.4 - 0.3\)
\(x = 0.1\) (10 cents)

Answer:

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