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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.

Respuesta :

mergl
200x+400y=80
150x+350y=67.5

200x+400y=80
200x=80-400y
x=0.4-2y
150(0.4-2y)+350y=67.5
60-300y+350y=67.5
50y=7.5
y=0.15 or 15 cents per text
200x+400y=80
200x+400(0.15)=80
200x+60=80
200x=20
x=0.1 or 0.10 per minute
So each text costs 5 cents more than each anytime minute

facundo3141592

We want to find the cost for each text message and anytime minutes, and we will get that by solving a system of equations.

  • Each text message costs $0.15
  • Each anytime minute costs $0.10

Then the correct statement is "Each text message costs 5 cents more than each anytime minute."

Finding and solving a system of equations.

First, we need to define the variables:

  • x = price of a text message.
  • y = price of an anytime minute.

We can write the given information as:

200*y + 400*x = $80.00

150*y + 350*x = $67.50

To solve the system now we need to isolate one of the variables in one of the equations, I will isolate y on the first one:

200*y = $80.00 - 400*x

y = ($80.00 - 400*x)/200 = $0.4 - 2*x

Now we can replace that in the other equation:

150*($0.4 - 2*x) + 350*x = $67.50

Now we can solve this for x.

$60 - 300*x + 350*x = $67.50

$60 + 50*x = $67.50

50*x = $67.50 - $60 = $7.50

x = $7.50/50 = $0.15

So each text message costs 15 cents.

And from the equation:

y = $0.4 - 2*x = $0.4 - 2*$0.15 = $0.10

So each minute costs 10 cents.

Then the correct statement is:

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

If you want to learn more about systems of equations you can read:

https://brainly.com/question/13729904

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