If Z varies directly as X and inversely as Y, and Z = 9, when X = 5 and Y = 3, find X when Z = 18 and Y = 6
"If Z varies directly as X and inversely as Y" ---> z =k(x/y)
when z=9, x=5,y=3
9 = k(5/3)
5k = 27
k = 27/5
So we have z = (27/5)(x/y)
for z=18, y = 6
18 = (27/5)(x/6)
27x = 540
x = 20
To find the value of X when Z = 18 and Y = 6, we can use the concept of direct and inverse variation.
Let's start by understanding the relationship between Z, X, and Y. When Z varies directly as X, it means that Z and X are directly proportional to each other. This can be represented as Z = kX, where k is the constant of variation. Similarly, when Z varies inversely as Y, it means that Z and Y are inversely proportional to each other. This can be represented as Z = k/Y.
To solve the problem, we need to find the value of X when Z = 18 and Y = 6. We know that Z = 9 when X = 5 and Y = 3. Using this information, we can find the value of k.
First, let's use the direct variation statement Z = kX. When Z = 9 and X = 5, we can plug in these values to find k: 9 = k * 5.
Dividing both sides of the equation by 5, we get k = 9/5.
Next, let's use the inverse variation statement Z = k/Y. When Z = 9 and Y = 3, we can plug in these values to find k: 9 = k/3.
Multiplying both sides of the equation by 3, we get k = 27.
Now that we have the value of k, we can use it to find the value of X when Z = 18 and Y = 6.
Using the direct variation equation Z = kX, we plug in the values: 18 = (9/5) * X.
To solve for X, we can multiply both sides of the equation by 5/9: X = 18 * (5/9).
Simplifying, we get X = 10.
Therefore, when Z = 18 and Y = 6, X is equal to 10.