Answer:
\(y =8 \cdot \frac{wx}{z}\)
Step-by-step explanation:
Joint variation says that:
If y varies jointly with x and inversely with z
i.e,
\(y \propto x\)
\(y \propto \frac{1}{z}\)
then the equation is in the form of :
\(y = k\frac{x}{z}\) where, k is the constant of variation.
As per the statement:
Suppose that y varies jointly with w and x and inversely with z
by definition of joint variation we have;
\(y = k\frac{wx}{z}\) ......[1]
It is given that: y = 400 when w = 10 , x = 25 and z = 5
Substitute in [1] we have;
\(400 = k \cdot \frac{10 \cdot 25}{5}\)
Simplify:
\(400 = 50k\)
Divide both sides by 50 we have;
8 = k
or
k = 8
⇒\(y =8 \cdot \frac{wx}{z}\)
Therefore, the equation that models the relationship is, \(y =8 \cdot \frac{wx}{z}\)
