Question

the variable z is directly proportional to x, and inversely proportional to y. when x is 9 and y is 6, z has the value 19.5. what is the value of z when x=14, and y=7

Answer 1

Answer: Z=30.8 when X=14 and Z=16.7 when Y=7

Explanation:

Z is directly proportional to X: Z=K*X, Where K is a constant

Z is inversely proportional to Y:
`Z=(K_(1) )/(Y)` where
`K_(1)` is another constant.

When Z=19.5 , X=9 , Using this condition we find K value

19.5=K*9 so, K=
`K=(19.5)/(9)`=2,2

When Z=19.5 , Y=6 , Using this condition we find
`K_(1)` value

19.5=
`(K_(1) )/(6)` so,
`K_(1)`=19.5*6=117

So, When X=14, Z= 2.2*14=30.8

When Y=7 Z=
`(117)/(7)`=16.7