Linear Inequality Word Problems

Question

An excess of nitrogen in fertilizer can damage lawns. Experts recommend that the amount of nitrogen applied to a lawn not exceed 1 pound (lb) of nitrogen per 1,000 square feet (ft²) of lawn. Renata, an avid gardener, has already purchased fertilizer containing 2.5 lb of nitrogen for her 7,000 ft² lawn. If she purchases additional fertilizer that contains 20% nitrogen by weight, how many pounds of the new fertilizer can she apply together with the previously purchased fertilizer without exceeding the recommended limit?

Answer 1

Here's another way.

She has a 7,000 sq ft lawn. The guidelines allow for no more than 1# N per 1,000 sq ft, so the maximum amount of N for her lawn is 7#. She already has 2.5#, so she can add as much as 7 - 2.5, or 4.5#.

How much add'l fertilizer can she buy if she needs 4.5# of N and it contains 20% N by weight? 0.2x = 4.5 -> x = 4.5/0.2 = 22.5# more.

Answer 2