You are an AI assistant to help me solve math problem.
I first give you an original question with an unknown variable $X$, You help me determine the value of $X$.
Follow the given examples and answer the question.

Question: On a map, a 12-centimeter length represents $X$ kilometers.  A 17-centimeter length represents 102 kilometers. What is the value of unknown variable $X$?
A: Let's think step by step.
To solve this problem, we need to determine the value of X, which represents the number of kilometers represented by a 12-centimeter length on the map.
We know that a 17-centimeter length represents 102 kilometers. Let's find out the ratio of kilometers to centimeters:
102 kilometers / 17 centimeters = 6 kilometers per centimeter
Now, we can calculate the value of X:
12 centimeters * 6 kilometers per centimeter = 72 kilometers
Therefore, the value of the unknown variable X is 72 kilometers.
The value of X is 72.

Question: If the sum of the squares of nonnegative real numbers $a,b,$ and $c$ is $39$, and $ab + bc + ca = X$, the sum of $a$, $b$, and $c$ is 9. What is the value of unknown variable $X$?
A: Let's think step by step.
We know that the sum of the squares of the three nonnegative real numbers is 39:
a^2 + b^2 + c^2 = 39
We also know that the sum of the three numbers is 9:
a + b + c = 9
To find the value of X, which represents the value of ab + bc + ca, we can use the following identity:
(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
Substituting the given values:
9^2 = 39 + 2X
81 = 39 + 2X
2X = 81 - 39
2X = 42
X = 42 / 2
X = 21
The value of X is 21.

Question: The mean of $5,8$ and $17$ is equal to the mean of $X$ and $y$. The value of $y$ is 8. What is the value of unknown variable $X$?
A: Let's think step by step.
We are given that the mean of 5, 8, and 17 is equal to the mean of X and y. We know that y is equal to 8. Let's denote the mean of X and 8 as M.
The mean of 5, 8, and 17 is given by:
(5 + 8 + 17) / 3 = 30 / 3 = 10
We are told that this mean is equal to the mean of X and 8, so we can set up the equation:
M = (X + 8) / 2
Since M is equal to 10, we can substitute it into the equation:
10 = (X + 8) / 2
To solve for X, we can multiply both sides of the equation by 2:
20 = X + 8
Subtracting 8 from both sides gives us:
X = 20 - 8
X = 12
The value of X is 12.

Question: A taxi ride costs \\$1.50$ plus $\\$0.25$ per mile traveled.  How much, in dollars, a $X$ mile taxi ride costs 2.75. What is the value of unknown variable $X$?
A: Let's think step by step.
We are given that a taxi ride costs $1.50 plus $0.25 per mile traveled. Let's denote the cost of a taxi ride as C and the number of miles traveled as X.
According to the given information, the cost C can be calculated using the formula:
C = $1.50 + $0.25X
We are also given that the cost of a taxi ride is $2.75. We can set up the equation:
$2.75 = $1.50 + $0.25X
To solve for X, we can subtract $1.50 from both sides of the equation:
$2.75 - $1.50 = $0.25X
Simplifying the left side gives us:
$1.25 = $0.25X
To isolate X, we can divide both sides of the equation by $0.25:
$1.25 / $0.25 = X
Simplifying the left side gives us:
5 = X
The value of X is 5.

Question: There are 6 ways to put 5 balls in $X$ boxes if the balls are not distinguishable but the boxes are. What is the value of unknown variable $X$?
A: Let's think step by step.
We are given that there are 6 ways to put 5 balls in X boxes, where the balls are not distinguishable but the boxes are.
To solve for X, we need to find the number of ways to distribute the balls among the boxes.
This problem can be solved using a combinatorial approach, specifically using stars and bars.
Since the balls are not distinguishable, we can think of them as stars. We need to distribute these stars among the X boxes, which can be represented by bars.
To distribute 5 stars among X boxes, we need X-1 bars to separate the boxes.
So, we have a total of 5 stars and X-1 bars, which gives us a total of 5 + (X-1) = X + 4 objects.
We need to select the positions of the stars among the X + 4 objects, which can be done in (X + 4 choose 5) ways.
Given that there are 6 ways to put the balls in the boxes, we can equate it to the calculated number of ways:
(X + 4 choose 5) = 6
To find the value of X, we can try different values until we find a combination that satisfies the equation.
By testing different values, we find that X = 2 satisfies the equation:
(2 + 4 choose 5) = 6
(6 choose 5) = 6
6 = 6
The value of X is 2.

Question: If $x - y = X$ and $x + y = 6$, The value of $y$ is -3. What is the value of unknown variable $X$?
A: Let's think step by step.
We are given that x - y = X and x + y = 6. We also know that y is equal to -3.
We need to find the value of X, which represents the difference between x and y.
To solve this, we can add the two given equations together:
(x - y) + (x + y) = X + 6
Simplifying the left side gives us:
2x = X + 6
To isolate X, we can subtract 6 from both sides of the equation:
2x - 6 = X
Since we know that y is equal to -3, we can substitute it into the equation x + y = 6:
x + (-3) = 6
Simplifying gives us:
x - 3 = 6
To solve for x, we can add 3 to both sides of the equation:
x = 6 + 3
x = 9
Now we can substitute the value of x into the equation 2x - 6 = X:
2(9) - 6 = X
18 - 6 = X
12 = X
The value of X is 12.

Question: The sum of the first $X$ odd positive integers is 100. What is the value of unknown variable $X$?
A: Let's think step by step.
We are given that the sum of the first X odd positive integers is 100.
The sum of the first X odd positive integers can be calculated using the formula:
Sum = X^2
We need to find the value of X that makes the sum equal to 100.
Setting up the equation:
X^2 = 100
To solve for X, we can take the square root of both sides of the equation:
sqrt(X^2) = sqrt(100)
Simplifying gives us:
X = 10
The value of X is 10.

Question: The sum of two numbers is $X$. Their difference is $4$. The larger of the two numbers is 17. What is the value of unknown variable $X$?
A: Let's think step by step.
We are given that the sum of two numbers is X and their difference is 4. We also know that the larger of the two numbers is 17.
Let's denote the two numbers as A and B, where A is the larger number.
From the given information, we can set up two equations:
A + B = X (equation 1)
A - B = 4 (equation 2)
We know that A is equal to 17, so we can substitute it into equation 2:
17 - B = 4
To solve for B, we can subtract 17 from both sides of the equation:
-B = 4 - 17
-B = -13
Multiplying both sides by -1 gives us:
B = 13
Now we can substitute the value of B into equation 1 to find X:
A + 13 = X
Substituting A = 17, we get:
17 + 13 = X
30 = X
The value of X is 30.