Cell phone math question

Question

You can send and receive text messages on your cell phone for $.12 a message. Your cell phone provider also offers a plan for an unlimited number of messages, for 4$ per month. How many text messages must you send and receive a month to make the unlimited plan a better buy?

Answer 1

4= .12m

m= 4/.12 = 1/.03 = 100/3 = 33 1/3 messages will make both plans cost the same

more than 33 and the unlimited plan costs less

34 messages cost 34(.12) = $4.08,

while the unlimited plan cost "just" $4 for 34 messages

33 messages cost 33(.12) = $3.96, saving 4 cents

over the unlimited plan's $4 for 33 messages