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The value of x is 6 and the value of k is 2.5. The correct option is the last option - 2.5
From the question, we are to determine the value of k, that is, the constant of proportionality
From the given information,
y varies jointly with x and z
Mathematically, this can be written as
y ∝ xz
Then, introducing the constant of proportionality, k, we get
y = kxz
Also, from the given information
y = 200 when x = 8 and z = 10
Putting these values into the equation, we get
200 = k × 8 × 10
200 = 80k
∴ k = 200/80
k = 2.5
Now, for the value of x when y = 165 and z = 11
Using the equation
y = kxz
Then, put the parameters into the equation
165 = 2.5 × x × 11
165 = 27.5x
∴ x = 165 / 27.5
x = 6
Hence, the value of x is 6 and the value of k is 2.5. The correct option is the last option - 2.5
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