Many fertilizers are given an NPK rating based on the percentages of the three major plant nutrients they contain: nitrogen (N), phosphorous (P), and potassium (K). For example, a fertilizer with an NPK rating of $5-7-3$ contains $5$ percent nitrogen, $7$ percent phosphorous, and $3$ percent potassium. A farmer has two fertilizers: fertilizer A, with an NPK rating of $20-10-10$, and fertilizer B, with an NPK rating of $50-13-16$. If the farmer mixes the two fertilizers such that the mixture contains $30$ percent nitrogen, what is the sum of the percentages of phosphorous and potassium in the mixture?

Wait, is it really as simple as just using the nitrogen percentages to find the ratio? I feel like I'm missing something because the answer came out too clean for a 700-level question.

Took me a sec to realize the P and K percentages in the mixture are just weighted averages of the two fertilizers, same as nitrogen. Once I got the ratio from N, it was straightforward. Nice problem.

Can someone explain why we can ignore the fact that the percentages don't add up to 100? Like 20+10+10 is only 40% and 50+13+16 is 79%. That's throwing me off.

This one was tricky because the answer choices include 14.5 and 28, which are half/double of each other, so if you mess up the ratio you might still land on a trap. I had to double-check my work.