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 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 1

Each text costs 5 cents more than each anytime minute.

Extra equations for you:

200x+400y=80

150x+350y=67.5

Answer 2

Answer : The true statement is, Each text message costs 5 cents more than each anytime minute.

Step-by-step explanation :

Let the anytime minutes be, x and text messages be, y.

As we are given that a month he used 200 anytime minutes and 400 text messages, and paid $80.00. The equation will be:

`200x+400y=80.00` ...........(1)

`x=(80.00-400y)/(200)` ............(A)

And,

As we are given that a month he used 150 anytime minutes and 350 text messages, and paid $67.50. The equation will be:

`150x+350y=67.50` ...........(2)

Now solving these two equation by substitution method by putting equation A in equation 2, we get:

`150x+350y=67.50`

`150* ((80.00-400y)/(200))+350y=67.50`

`3* ((80.00-400y)/(4))+350y=67.50`

`(240-1200y)/(4)+350y=67.50`

`240-1200y+1400y=270`

`200y=30`

`y=(30)/(200)`

`y=\$ 0.15`

As we know that, $ 1 = 100 cents

So, $ 0.15 = 15 cents

y = 15 cents

Now put the value of 'y' in equation A, we get:

`x=(80.00-400y)/(200)`

`x=(80.00-400(15))/(200)`

`x=10`

x = 10 cents

As per given statements we conclude that, Each text message costs 5 cents more than each anytime minute is the correct statements.

Proof :
`y=5cents+x`

x = 10 cents

`y=5cents+10cents=15cents`

Thus, the true statement is, Each text message costs 5 cents more than each anytime minute.