The latest online craze is a new game, Khan on Seven. You get 100100100 points for playing the game. In addition, you get 505050 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.
The Correct Answer and Explanation is:
To find out how many seven-letter words Sal needs to create to break the record, let’s define the known values from the question:
Given:
- Base score for playing the game: 100100100 points
- Points per seven-letter word: 505050 points
- Target score to break the record: 18,000 points
Wait a minute — there is a problem here.
The base score mentioned is 100100100 points, which is over 100 million points, and Sal only needs 18,000 points to break the record. This cannot be correct as written, because he already has over 100 million points just for playing.
Let’s assume there’s a typo or formatting error in the question. Most likely, the numbers are 100, 100, and 100 points for base play, and 50, 50, and 50 points for each seven-letter word — that is, the actual points are:
- Base score: 100 points
- Points per word: 50 points
- Target: 18,000 points
Let’s solve under this assumption.
Step 1: Base Score
Sal gets 100 points automatically.
Step 2: Let’s say Sal makes x seven-letter words.
Each word gives 50 points, so the total additional points are 50x.
Step 3: Total Score
Total score = Base score + Word points = 100 + 50x
Step 4: Set up inequality
We want:
$$
100 + 50x \geq 18000
$$
Subtract 100:
$$
50x \geq 17900
$$
Divide by 50:
$$
x \geq \frac{17900}{50} = 358
$$
✅ Final Answer:
Sal needs to make at least 358 seven-letter words to break the record.
Explanation (300+ words):
To determine how many seven-letter words Sal must create to surpass the 18,000-point record, we first interpret the game’s scoring system. The question states that Sal earns 100100100 points for playing the game and 505050 points for each valid word. However, these numbers are most likely formatting errors — the repetition suggests that the real values are 100 points for playing and 50 points per word. Otherwise, the base score would already far exceed the goal.
Assuming that, we start by recognizing that Sal begins with a base of 100 points. Then, he earns 50 points for every seven-letter word formed. If he forms x such words, his total score becomes:
$$
\text{Total score} = 100 + 50x
$$
We want this total to be at least 18,000 to break the record. That sets up the inequality:
$$
100 + 50x \geq 18000
$$
Subtracting the base score:
$$
50x \geq 17900
$$
Dividing both sides by 50:
$$
x \geq 358
$$
This means Sal must form at least 358 seven-letter words to reach or exceed the record score. If he forms fewer than that, his total score will fall short.
This kind of problem involves translating a real-world scenario into an algebraic inequality, solving it, and interpreting the result in the context of the game. It’s a great example of practical math — using arithmetic and algebra to solve everyday problems.