We want to find the value of $X$ in the given situation.
We are given that the number of students who study Spanish is between $X$ percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent.
To find the smallest number of students who could study both languages, we need to consider the minimum percentages for both languages.
The smallest number of students who study both languages is the minimum of the two percentages.
Let's call the minimum percentage for Spanish $S_{min}$ and the minimum percentage for French $F_{min}$.
$S_{min} = X$
$F_{min} = 30$
The smallest number of students who could study both languages is given by the equation:
$m = \frac{S_{min} + F_{min} - 100}{100} \times 2001$
Substituting the values of $S_{min}$ and $F_{min}$, we have:
$m = \frac{X + 30 - 100}{100} \times 2001$
$m = \frac{X - 70}{100} \times 2001$
To find the largest number of students who could study both languages, we need to consider the maximum percentages for both languages.
The largest number of students who study both languages is the maximum of the two percentages.
Let's call the maximum percentage for Spanish $S_{max}$ and the maximum percentage for French $F_{max}$.
$S_{max} = 85$
$F_{max} = 40$
The largest number of students who could study both languages is given by the equation:
$M = \frac{S_{max} + F_{max} - 100}{100} \times 2001$
Substituting the values of $S_{max}$ and $F_{max}$, we have:
$M = \frac{85 + 40 - 100}{100} \times 2001$
$M = \frac{25}{100} \times 2001$
$M = \frac{1}{4} \times 2001$
$M = \frac{2001}{4}$
$M = 500.25$
Since $M$ represents the number of students, it must be a whole number. Therefore, we can round down $M$ to the nearest whole number:
$M = 500$
We are given that $M - m = 298$, so we can write:
$500 - m = 298$
Subtracting 298 from both sides of the equation, we find:
$m = 202$
To find the value of $X$, we need to substitute the value of $m$ into the equation for $m$:
$202 = \frac{X - 70}{100} \times 2001$
Dividing both sides of the equation by 2001, we get:
$\frac{202}{2001} = \frac{X - 70}{100}$
Cross-multiplying, we have:
$100 \times 202 = 2001 \times (X - 70)$
$20200 = 2001X - 140070$
Adding 140070 to both sides of the equation, we find:
$160270 = 2001X$
Dividing both sides of the equation by 2001, we get:
$X = \frac{160270}{2001}$
$X = 80$
The value of $X$ is 80.
The answer is: 80
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Each of the $2001$ students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between X percent and $85$ percent of the school population, and the number who study French is between $30$ percent and $40$ percent. Let $m$ be the smallest number of students who could study both languages, and let $M$ be the largest number of students who could study both languages. Find $M-m$.

If we know the answer to the above question is 298, what is the value of unknown variable X?

### Answer:
