y varies directly as x and inversely as the square of z

Question

y varies directly as x and inversely as the square of z. y equals 88y=88 when x equals 36x=36 and z equals 3z=3. Find y when x equals 75x=75 and z equals 5z=5.

Answer 1

y varies directly as x: y = kx

y varies inversely as the square of z: y = k/z²

 

Combining the two with k being constant since it is a "constant", it will be:

 

y = kx/z² (working equation)

 

For the first condition, it gives:

 

y = 88

x = 36

z = 3

 

Substituting to the working equation:

 

88 = k(36)/(3²); Solving for k, k = 22 *k means constant hence using this equation should always has a value of 22 for k*

 

For the second condition:

 

x = 75

z = 5

and as I mentioned above, k = 22.

 

Solving for y:

 

y = 22(75)/(5²)

 

y = 66 *This type of questions always have the same pattern, 1st condition to solve for k then the 2nd condition to find whatever*