Question

On January 1, 2000, there were 175,000 tons of trash in a landfill that had a capacity of 325,000 tons. Each year since then, the amount of trash in the landfill increases by 7.500 tons. If y represents the time, in years, after January 1, 2000.
Required:
What inequalities describes the set of years where the landfill is at or above capacity?

Answer 1

Answer: 175,000 + 7,500y ≥ 325,000

Explanation:

On January 1, 2000, there are 175,000 tons of trash in the landfill.

This increases by 7,500 tons every year with y representing the number of years.

This means that in a given year, the amount of trash in the landfill is:

= 175,000 + 7,500y

The capacity is 325,000 tons. In years where the landfill will be at or above capacity, the result of the formula above will be greater than 325,000 tons.

The relevant inequality therefore is:

175,000 + 7,500y ≥ 325,000