X3Y+5YX = 1,33X
In the correctly worked addition problem above, X and Y represent 2 different digits. What digit does X represent?
a. 0
b. 1
c. 4
d. 8
e. 9
To determine the value of X in the equation X3Y + 5YX = 1.33X, we will follow the steps to solve the equation.
1. Start by expanding the terms:
X * 100 + 3 * 10 + Y + 5 * Y * 10 + X = 1.33 * X
2. Simplify the equation by combining like terms:
100X + 30 + Y + 50Y + 10X = 1.33X
3. Combine the X terms on one side of the equation:
100X + 10X - 1.33X = -30 - 50Y - Y
4. Simplify the equation further:
109.67X = -30 - 51Y
Now, in order to find the value of X, we need to consider the answer choices given.
a. If X = 0, we would have 109.67 * 0 = -30 - 51Y, which is not possible since multiplying by zero gives zero.
b. If X = 1, we would have 109.67 * 1 = -30 - 51Y, which is still not possible.
c. If X = 4, we would have 109.67 * 4 = -30 - 51Y. This equation does not result in an integer value for Y.
d. If X = 8, we would have 109.67 * 8 = -30 - 51Y, which also does not yield an integer value for Y.
e. If X = 9, we would have 109.67 * 9 = -30 - 51Y, which again does not result in an integer value for Y.
Therefore, none of the given answer choices for X (a, b, c, d, e) satisfy the equation. It seems there might be an error in the equation provided or in the answer choices, as it is not possible to find a single value for X and Y that satisfies the equation.