Help on Inequality word problem

Question

Joeys parents kicked him off their cellphone plan, so he is researching new plans. During his research, Joey found that AT&T charges $39.99 per month for 450 minutes, plus $0.45 for every minute over the limit. Write and solve an inequality to find he possible numbers of minutes Joey can use per month if he is willing to spend at most $55 per month.

Answer 1

Let m = minutes past 450. Here's what we know:

.45m + 39.99 ≤ 55 (the plan cannot go above $55)

 

Now to isolate m. Start by rounding 39.99 to 40 and then subtract that from both sides:

.45m ≤ 15

Divide both sides by .45:

m ≤ 33.3333....

Joey's not going to be charged part of a minute, so round that down to 33. Add that to the base number of minutes for the plan, and you'll have your final answer