The value of x cannot be determined from “50 100” alone; please provide the equation or context. Common interpretations include a proportion such as 50/x = x/100, or a relation where x/50 = 100/x, etc., so please specify the intended relationship.
Explanation
To determine x, we need a specific relationship that involves 50, 100, and x. Without an equation, x can be any value. Below are two common interpretations and how to solve them when they are intended:
- Proportion 1: 50/x = x/100
Cross-multiply: 50·100 = x^2 → 5000 = x^2
Thus x = ±√5000 ≈ ±70.71. In many contexts x is taken as the positive root, so x ≈ 70.71.
- Proportion 2: x/50 = 100/x
Cross-multiply: x^2 = 50·100 = 5000
Thus x = ±√5000 ≈ ±70.71. Again, the positive root is commonly used when x represents a positive quantity.
- Linear/other interpretations: If the problem means something like a linear relation or a midpoint (e.g., x is the average of 50 and 100), the result would be different (for the midpoint, x = (50 + 100)/2 = 75). The exact value depends on the specified equation.
Key Points
- Without the exact equation or context, x cannot be uniquely determined.
- Providing the intended relationship (proportion, equation, or condition) allows a precise solution.
- For common proportional forms like 50/x = x/100 or x/50 = 100/x, the solution yields x = ±√5000 ≈ ±70.71 (often taking the positive root).