SOLUTION: if 'w' varies jointly with 'x' and 'y', and inversely as the square of 'z', how would 'w be affected if 'x' is tripled and both 'y' and 'z' are doubled?

Question 1174492: if 'w' varies jointly with 'x' and 'y', and inversely as the square of 'z', how would 'w be affected if 'x' is tripled and both 'y' and 'z' are doubled?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the base formula is:

w = (k * x * y / z^2)

if x is tripled and y is doubled and z is doubled, the formula becomes:

w = k * 3 * x * 2 * y / (2 * z)^2

simplify to get:

w = 6 * k * x * y / (4 * z^2)

rearrange the equation to get:

w = (6 / 4) * (k * x * y / z^2)

simplify to get:

w = 1.5 * (k * x * y / z^2).

the value of w should be 1.5 times what it was originally.

to see how this works, let k = 5 and w = 2 and y = 4 and z = 6.

thee values were picked randomly.

the original equation becomes:

w = 5 * 2 * 4 / 6^2 = 40/36 = 1.1111111.....

the revised equation becomes:

w = 5 * 3 * 2 * 2 * 4 / 12^2

simplify to get:

w = 240 / 144 = 1.6666666....

1.1111111..... * 1.5 = 1.666666....

this confirms the solution is correct as far as i can tell.

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