To determine the equation that models the relationship between the variables y, w, x, and z, we start by understanding the principle of joint and inverse variation.
When we say that y varies jointly with w and x, it means that y is proportional to the product of w and x. Additionally, since y varies inversely with z, it means that y is also inversely proportional to z.
Combining these relationships gives us the following equation:
y = k * (w * x) / z
Here, k is the constant of proportionality that we need to determine.
Given the values:
- w = 8
- x = 25
- z = 5
- y = 360
We can substitute these values into the equation to solve for k:
360 = k * (8 * 25) / 5
First, calculate the product on the right side:
- 8 * 25 = 200
Now simplify the equation:
360 = k * (200 / 5)
Now calculate 200 divided by 5:
- 200 / 5 = 40
This gives us:
360 = k * 40
To find k, divide both sides by 40:
k = 360 / 40
Calculating this gives:
- k = 9
Now that we have determined k, we can substitute it back into our initial equation:
y = 9 * (w * x) / z
This is the equation that models the relationship where y varies jointly with w and x, while inversely with z.
In conclusion:
The final equation is:
y = 9 * (w * x) / z