Janice is going on vacation and needs to leave her dog at a kennel. Nguyen'ts Kennel charges $15/day plus $20 processing fee. The Pup Palace charges $12/day and a $35 processing fee. After how many days is the Pup Palace Kennel cheaper than Nguyen's?
More than 5 days makes Pup Palace the better deal.
This requires you to solve an inequality. You create small expressions for the cost of each kennel and set up the inequality so that the "Pup Palace" expression is less than the "Nguyen's" expression.
Call the number of days "n". Each kennel has a cost portion that will depend on the number of days, and a fixed portion that will not.
For Pup Palace, the cost can be written as 12n + 35
For Nguyen's, the cost is written as 15n + 20
Now, set up the inequality so that the Pup Palace expression is less than the Nguyen's expression:
12n + 35 < 15n + 20 (That is the most difficult part done!)
To solve this, we "collect like terms". First subtract 12n from both sides:
35 < 3n + 20
Now, subtract 20 from each side.
15 < 3n
Divide each side by 3:
5 < n
We should read this as n > 5 (is that okay?) which tells us that for any stay greater than 5 days, Pup Palace is the better deal!
(By the way, you should check that your answer is correct. Six days means Pup Palace costs $107, while Nguyen's is $110.)