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
since in the ones place, X+Y=X, Y=0 and we have
X30+50X = 133X
so, X3+50 = 133 or,
10X+3 + 50 = 133
10X = 80
X = 8
To determine the value of X in the equation X3Y + 5YX = 1.33X, we can use algebraic reasoning. Let's break it down step by step:
1. Expand the terms: X3Y + 5YX = 1.33X
2. Rearrange the equation to isolate the X terms on one side: 5YX - 1.33X = -X3Y
3. Factor out the X from the left side: X(5Y - 1.33) = -X3Y
4. Divide both sides of the equation by (5Y - 1.33): X = (-X3Y) / (5Y - 1.33)
Now, to determine the value of X, we need to find suitable values for Y so that the equation is satisfied. We know that X and Y represent two different digits, which means that X and Y must be integers from 0 to 9. Since X cannot be zero (otherwise, the number would start with a leading zero), we can test different integer values for Y to see what works.
By trying different values for Y in the equation, we find that Y = 9 satisfies the equation:
X = (-X3(9)) / (5(9) - 1.33)
Now, substitute Y = 9 into the equation:
X = (-X3(9)) / (5(9) - 1.33)
Next, simplify the equation:
X = (-27X) / (45 - 1.33)
To eliminate the fraction, multiply both sides of the equation by (45 - 1.33):
X(45 - 1.33) = -27X
Simplify:
43.67X = 0
Divide both sides of the equation by 43.67:
X = 0
Therefore, X represents the digit 0.
The correct answer is (a) 0.