Question

The latest online craze is a new game, Khan on Seven. You get
\[100\] points for playing the game. In addition, you get
\[50\] points for each seven-letter word you make with the ten letters you receive. Sal wants to break the record, and he needs
\[18{,}000\] or more points to do so.
Write an inequality to determine the number of seven-letter words,
\[w\], Sal could make to break the record.

Answer 1

Let w be the number of seven-letter words. Sal's total points are 100 + 50w. He needs at least 18,000, so

100 + 50w ≥ 18,000.

Solving: 50w ≥ 17,900 → w ≥ 358.

So Sal must make at least 358 seven-letter words (w ≥ 358).