To solve this problem, we start by understanding the concept of inverse variation. If a varies inversely as b, it means that as one of the variables increases, the other decreases. Mathematically, this relationship can be represented as:
a × b = k
where k is a constant.
1. **Determine the constant (k):** Given that a = 3 when b = 4, we can plug these values into the equation to find k.
3 × 4 = k
This simplifies to:
k = 12
2. **Express the relationship:** Now that we know the constant, we can express the relationship between a and b as:
a × b = 12
3. **Find b when a = 48:** We need to find the value of b when a = 48. Using the equation we obtained:
48 × b = 12
To isolate b, we can divide both sides of the equation by 48:
b = \frac{12}{48}
This simplifies to:
b = \frac{1}{4}
Thus, the value of b when a = 48 is:
b = 0.25
In summary, when a = 48, b evaluates to 0.25.