Algebra 1 question

Question

At an amusement park there’s only enough room for 4500 people to be in it at any time. The manager has also worked out that there needs to be 2800 people in the park to make a profit after all the overhead costs and employees pay. If people are entering the park at a rate of 12 people a minute and there are 850 people in the park currently, between how many minutes should the door stay open to let guests in.

a) Translate the scenario above into a compound inequality involving the number of minutes that the door has been open. Take into account both the fact that there must be a minimum of 2800 people and a maximum of 4500 people.

Answer 1

" Take into account both the fact that there must be a minimum of 2800 people and a maximum of 4500 people."

If your minimum is 2800 and maximum is 4500 your expression is going to be squished in between the min and max in an equality like this

2800 ≤ ..... ≤ 4500

We know the expression in the middle must be greater than or equal to the minimum (that's why the open end (or alligator) is pointing to it - you may have heard the alligator eats the bigger number. So that reads that the expression in the middle is greater than or equal to 2800. Then if the maximum is 4500 you can have 4500 you just can't go over it, so the expression in the middle would be less than or equal to your maximum.

"people are entering the park at a rate of 12 people a minute and there are 850 people in the park currently"

This is going to be your "expression in the middle" I keep talking about.

Your rate of 12 a minute - or you could say 12 per minute - refers to multiplication. You don't know the number of minutes so that will be your variable- let's use m.

Also there were already 850 people in the park so you need to add that to your rate. 850 + 12m (12m is 12 multiplied by the number of minutes, m). Now insert that into your compound inequality, and you get

2800 ≤ 850 + 12m ≤ 4500

Let me know if this helped!