Question

The Call First cell phone company charges 535 per month and an additional 50.16 for each text message sent during the month. Another cell phone company, Cellular Plus, charges $45 per month and an additional $0.08 for each text message sent during the month a. How many text messages would have to be sent in a month to make both plans cost the same?

Answer 1

Answer:

(The problem doesn't have solution as stated, i think you press 5 instead of $ on 535 and 50.16. With this as initial prices, they would never cost the same.)

• 125 messages.

Step-by-step explanation:

We can express the charge c of the Call First company as:

$c_{cf}(m) = \ 35 + 0.16 \frac{\ }{message} \ m$

where m is the number of messages sent.

For Cellular plus

$c_{cp}(m) = \ 45 + 0.08 \frac{\ }{message} \ m$.

Now, for a number of messages m' the cost will be the same

$c_{cf}(m') = c_{cp}(m)$

$\ 35 + 0.16 \frac{\ }{message} \ m' = \ 45 + 0.08 \frac{\ }{message} \ m'$

Now, we can work the equation a little

$ 0.16 \frac{\ }{message} \ m' -  0.08 \frac{\ }{message} \ m'= \ 45 - \ 35$

$ (0.16 \frac{\ }{message} \  -  0.08 \frac{\ }{message}) \ m'= \ 10$

$ 0.08 \frac{\ }{message} \ m'= \ 10$

$ m'= \frac{ \ 10 }{  0.08 \frac{\ }{message} }$

$ m'= 125 \ messages$

So the number of messages that needs to be sent have make both plans cost the same is 125.