To solve this problem, we start by understanding the relationship where one variable varies inversely as another. In mathematical terms, this can be expressed as:
A × B = k
Here, k is a constant. From the problem, we know that when A is 3, B is 4. We can substitute these values into the equation to find the constant k:
3 × 4 = k
Calculating this gives us:
k = 12
Now that we have the constant k, we can use this to find the value of B when A is 48. We plug A = 48 into our inverse variation equation:
48 × B = 12
To isolate B, we divide both sides of the equation by 48:
B = 12 / 48
Calculating this gives:
B = 1/4
Therefore, when A is 48, the value of B is 1/4.