inequalities story problem

[puddintane]

Carollton has a population of 117823 and the population changes each year by +1170. Lakewood has a population of 141,301 and the change is-830. I'm supposed to figure out how long Carrollton's population will be less than Lakewood and round it to the nearest tenth. I just don't know what inequality I'm supposed to start out with. If I did, I could probably figure it out from there.

 

[Mrspi]

Carollton has a population of 141,301 and the population changes each year by +1170. Lakewood has a population of 141,301 and the change is-830. I'm supposed to figure out how long Carrollton's population will be less than Lakewood and round it to the nearest tenth. I just don't know what inequality I'm supposed to start out with. If I did, I could probably figure it out from there.

Hmmm...Carollton gains 1170 people each year. Lakewood starts with the same population as Carollton, and loses 830 people each year. So Carollton's population will be going UP while Lakewood's population is going down.

They have the same population now. Carollton's population goes UP and Lakewood's population goes DOWN. Common sense tells me that Carollton isn't EVER going to have a smaller population than Lakewood as long as these conditions continue.

If you want to write an inequality, you could do this:

Let t = number of years

Carollton's population in t years = 141301 + 1170t
Lakewood's population in t years = 141301 - 830t

You want to know how long Carollton's population is going to be less than Lakewood's:

141301 + 1170t < 141301 - 830t

I'm guessing that perhaps you did not type the problem correctly....but maybe seeing this setup will help you figure it out.

You could try solving that..and you should find that Carollton's population is not going to be less than Lakewood's population at any time in the future (as long as this growth pattern continues).

 

[puddintane]

Your right, I typed the question wrong, but I think I can figure it out now. Arigato Gozaimasu​ (thank you very much)