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)

$x=\frac{80.00-400y}{200}$     ............(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:

$150x+350y=67.50$

$150\times (\frac{80.00-400y}{200})+350y=67.50$

$3\times (\frac{80.00-400y}{4})+350y=67.50$

$\frac{240-1200y}{4}+350y=67.50$

$240-1200y+1400y=270$

$200y=30$

$y=\frac{30}{200}$

$y=\ 0.15$

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:

$x=\frac{80.00-400y}{200}$

$x=\frac{80.00-400(15)}{200}$

$x=10$

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.

Answer 3

the answer is A)