X+y=1545.55 x_y=1459.55 2x=3005.1 x=1502.55 z=1502.55+542.31=2046.86 x+y+z=1545.55+2046.86=3592.41

Given information:
- X is 1459.55 more than Y.
- X is 542.31 less than Z.
- The product of X and Y is 1545.55.

To find:
The values of X, Y, and Z.

Step 1: Assign variables to unknowns:
- Let Y = a (unknown value)
- X = a + 1459.55 (as X is 1459.55 more than Y)
- Z = X + 542.31 (as X is 542.31 less than Z)

Step 2: Express X and Z in terms of a:
- X = a + 1459.55
- Z = (a + 1459.55) + 542.31

Step 3: Substitute X and Z into the equation XY = 1545.55:
- (a + 1459.55) * a = 1545.55
- Simplify the equation: a^2 + 1459.55a = 1545.55

Step 4: Solve the quadratic equation:
- Rearrange the equation: a^2 + 1459.55a - 1545.55 = 0
- Apply the quadratic formula: a = (-b ± √(b^2 - 4ac)) / 2a
- In this case, a = 1, b = 1459.55, c = -1545.55
- Substitute the values: a = (-1459.55 ± √((1459.55)^2 - 4(1)(-1545.55))) / (2(1))

Step 5: Calculate the values of a:
- Use a calculator to evaluate the expression inside the square root: √(2130287.4025 + 6182.22) = √2136470.6225 = 1461.34
- Substitute the values: a = (-1459.55 ± 1461.34) / 2
- Solving for a gives two possible values: a = 1.395 or a = -1460.945

Step 6: Calculate the corresponding values of X and Z:
- For a = 1.395:
- X = a + 1459.55 = 1.395 + 1459.55 = 1460.945
- Z = (a + 1459.55) + 542.31 = 1460.945 + 542.31 = 2003.255
- For a = -1460.945:
- X = a + 1459.55 = -1460.945 + 1459.55 = -1.395
- Z = (a + 1459.55) + 542.31 = -1.395 + 542.31 = 540.915

Final answer:
The possible values for X, Y, and Z are:
1. X = 1460.945, Y = 1.395, Z = 2003.255
2. X = -1.395, Y = -1460