I need to learn vocabulary words for my Spanish exam. There are 500 words and the exam grade is the percentage of these words that I recall correctly. Assuming I will recall correctly the words I learn and assuming my guesses will not yield any points, what is the least number of words I should learn to get at least $85\%$ on the exam?
This problem involves finding the smallest number of words, let's call it $x$, such that the ratio of $x$ to 500 is at least 0.85. To isolate $x$, I can multiply both sides by 500, which gives me $x \geq 0.85 \times 500$. I can use a calculator or mental math to find that $0.85 \times 500 = 425$. Since $x$ has to be a whole number, the smallest possible value of $x$ is 425. This means I need to learn at least 425 words to get at least $85\%$ on the exam.

