Question

During one month of cell phone use, Noah used 200 anytime minutes and 400 text messages, and paid $80. the next month, he used 150 anytime minutes and 350 text messages, and paid $67.50. which statement is true?
a) each text message costs 5 cents more than each anytime minute
b) each anytime minute costs 10 cents more than each text message
c) a text message and an anytime minute each costs 25 cents
d) each text message costs double the amount of an anytime minute

Answer 1

Answer: a) each text message costs 5 cents more than each anytime minute

Step-by-step explanation:

Let x be the cost of anytime minutes and y be the cost of text messages.

Then for the first month, equation for the total amount Noah paid

$200x+400y=80\\\Rightarrow5x+10y=2..\text{[divide 20 on both sides]}\\\Rightarrow15x+30y=6....\text{[multiply 3 on both sides]}$...(1)

For the second month, equation for the total amount Noah paid

$150x+350y=67.5\\\Rightarrow15x+35y=6.75....\text{[divide 10 on both sides]}$....(2)

Now subtract equation (1) from equation (2), we get

$5y=0.75\\\Rightarrow\ y=0.15$

Put y=0.15 in (1), we get

$5x+10(0.15)=2\\\Rightarrow5x+1.5=2\\\Rightarrow\ x=\frac{2-1.5}{5}=0.10\\\Rightarrow\ x=0.10$

Thus, the cost of anytime minutes(x)= $0.10= 10 cents

and the cost of test messages(y)=$0.15=15 cents

Difference=15-10=5 cents

Hence,  each text message costs 5 cents more than each anytime minute.

Answer 2

The statement A is true since on forming the quadratic equations formed you will find the cost of a message being 15 cents and that of anytime as 10 cents.