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 increased by 7,500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?

• A. $325,000-7500\le y$
• B. $325,000\le 7500y$
• C. $150,000\ge 7500y$
• D. $175000+7500y\ge 325000$

Answer 1

The correct option is D $175000+7500y\ge 325000$

At the beginning of the year 2000, there is 175,000 tons of trash in the landfill. Each year since, an additional 7500 tons of trash is dumped every year. So, at the end of y years after the year 2000, the total amount of trash in the landfill is 175000 + 7500 y

Given that capacity of landfill is 325,000 tons. Hence, the set of years the landfill is at or above capacity is described by the following inequality

$175000+7500y\ge 325000$
Hence, D is the correct choice.