as given to us -

X = mean

M = median

Z = mode

and

[tex]\sf{\dfrac{X}{M} = \dfrac{9}{8}}[/tex]

[tex]\sf{X = \dfrac{9M}{8}}[/tex]

relation b/w mean , median and mode -

[tex]\sf{Mode = 3(median) - 2(mean)}[/tex]

Mode = 3(median) - 3(mean) + mean

Mode = 3(median - mean) + mean

Mode - mean = 3(median - mean)

Z - X = 3(M - X)

[tex]\sf{Z(1 - \dfrac{X}{Z}) = 3M(1 - \dfrac{X}{M})}[/tex]

Z(1 - X/Z) = 3M(1 - 9/8)

Z(1 - X/Z) = 3M(-1/8)

On putting value of X

[tex]\sf{Z(1 - \dfrac{9M}{8Z})= - \dfrac{3M}{8}}[/tex]

[tex]\sf{\dfrac{\cancel{Z}(8Z - 9M)}{8\cancel{Z}} = - \dfrac{3M}{8}}[/tex]

[tex]\sf{\dfrac{(8Z - 9M)}{\cancel{8}} = - \dfrac{3M}{\cancel{8}}}[/tex]

8Z - 9M = - 3M

8Z = - 3M + 9M

8Z = 6M

6M = 8Z

[tex]\sf{\dfrac{M}{Z} \: = \: \dfrac{8}{6} = \dfrac{4}{3}}[/tex]

[tex]\: M : Z \: = \: 4 : 3[/tex]

Verified answer

Answer:

hehe let's see

who will rock?

but m definitely sure that u r rocking