Question

If X is 2/3 of Y and Y is 3/4 Of Z, what is the ratio of Z:X?

Here is what I did:
X=2/3Y
Y=3/4Z

X=2/3(3/4Z) substituted Y
X=1/2 Z multiplied the fractions
2x=1z multiplied by 2

so z:x=1:2

but apparently the right answer is 2:1, so what did I do wrong?

Answer 1

you are correct upto x= 1/2z
divide all through by z
this gives you:
x/z = 1/2
or x:z = 1:2
or z:x = 2:1

Answer 2

you lost me at divide all through by z.

Answer 3

see, u got 2x = 1z right? now just divide throughout by x. what do u get?

Answer 4

so i should divide by x? then it's 2=z/x?

Answer 5

whatever you divide with, you'll get the right answer, so if you decide to divide by x then you have 2 =z/x, but isn't two the same as 2/1

Answer 6

exactly!
2 = z/x
or 2/1 = z/x
or 2:1 = z:x
got it?

Answer 7

nope I still don't get it why would you divide by the variable anyway?

Answer 8

u want x in the denominator right?

Answer 9

2x=1z is a ration doesn't that mean for every 2Xs there's 1Z

so the ratio of z:x is 1:2

Answer 10

what is wrong with what I just did?

Answer 11

are u confusing a ratio with the proportional sign?
see, a ratio means something divided by something. so z:x = z/x. is this clear?

Answer 12

2x=1z is correct, but remember you need a ratio, so you have to put like terms together. in your case (x,z) is one set of like terms and (2,1) is another, so what do you do to this equation to bring like terms to the same side?
can you please cross multiply x/z =1/2 and see what you get

Answer 13

2x=1z

Answer 14

ok i got it now, I have to get the variables together to make it right

Answer 15

thanks both of you

Answer 16

np^^