The Annual County Carnival is being held is summer and will last 5 and 1/2 days. Use this information and other given information to answer each question.

You are the owner of the biggest and newest roller coaster called "Gentle Giant". The roller coaster costs $6 to ride. The operator of the ride must pay $200 per day for the ride rental and $65 per day for a safety inspection. If you want to make a profit of at least $1,000 each day, what is the minimum number of people that must ride the roller coaster?

Write an inequality that can be used to find the minimum number of people, p, which must ride the roller coaster each day to make the profit.

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carlosego carlosego · Answer 1 · 2019-02-26T03:10:03+01:00

Answer:

[tex]6p - 65 -200\geq 1000[/tex]

[tex]p\geq 211\ people[/tex]

Step-by-step explanation:

To solve this problem you must follow the following procedure:

1. Group the costs:

$ 200 per day

$ 65 per day

2. Group the profits

$ 6 per person

3. The difference between the costs and the profit must be greater than or equal to $ 1000.

[tex]Profit - cost\geq 1000[/tex]

4. We call p the number of people who climb the roller coaster.

So:

[tex]6p - 65 -200\geq1000[/tex]

5. We clear p:

[tex]6p\geq 1000 +65 +200[/tex]

[tex]p\geq \frac{1265}{6}\\\\p\geq 210.83[/tex]

[tex]p\geq 211\ people[/tex]

211 people or more must climb the roller coaster to make a profit