Suppose that Y varies directly as X and inversely as Z, and Y 🟰 9 when X 🟰 12 and Z 🟰 4. Solve for Y when X 🟰 45 and Z 🟰 5.

1. Given that Y varies directly as X and inversely as Z , the relationship can be written as:

Y=k\times\frac{X}{Z}

2. Using the initial conditions Y = 9 , X = 12 , and Z = 4 , we can solve for k :

9=k\times\frac{12}{4}

9 = 3k

k = 3

3. Now substitute X = 45 , Z = 5 , and k = 3 into the equation:

Y=3\times\frac{45}{5}

Y = 3 \times 9

Y = 27

Answer: Y=27