Final answer:
In an inverse variation relationship, where y varies inversely as x, y equals 4.8 when x is 20 and x equals 16 when y is 6.
Step-by-step explanation:
The student's question involves inverse variation, where the product of two variables is constant. For inverse variation, the equation is represented as y = k/x, where k is the constant of variation. To solve part (a) and part (b), we will first find the value of k using the given values of x and y (x = 8, y = 12), and then use this constant to solve for y when x = 20 and for x when y = 6.
Find the constant of variation
To find k, we can plug in the given values into the inverse variation formula:
12 = k / 8
k = 12 × 8
k = 96
Solution for part (a)
Now we have to find y when x = 20:
y = 96 / 20
y = 4.8
Solution for part (b)
Next, to find x when y = 6:
6 = 96 / x
x = 96 / 6
x = 16
In conclusion, y equals 4.8 when x is 20, and x equals 16 when y is 6 in an inverse variation scenario.