Question

If `x:y = 5:2` and `y:z = 3:2`, what is the ratio of `x:z`?

Answer 1

`x/z= 15/4" " ->" " x:z=15:4`

Explanation:

To solve this you need to adopt the fraction style of ratio presentation

`x/y=5/2`

`y/z=3/2`

Need `x/z`

Consider `x/yxxy/z`

Write this as:

`(x xx y)/(yxx z)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As an example of what I am about to do consider `3xx2`. You have the same result if you reverse these numbers.

So `3xx2=2xx3=6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So `(x xx y)/(yxx z)" " =" "(x xx y)/(z xx y)" " =" " x/z xxy/y" " =" "x/z`

`color(white)(.)`

`=>x/z=" "x/y xxy/z" " =" " 5/2xx3/2" " =" " 15/4`

Answer 2

Alternative approach

`x:z" "->" "x/z=15/4`

Explanation:

`x/y=5/2` ..................................Equation(1)
`y/z=3/2`...................................Equation(2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From equation (2) `y=3/2z`

Consider equation(1)

Substitute for y giving

`x/y=5/2 " "->" "x/(3/2z)=5/2`

`2/3 x/z=5/2`

`x/z=3/2xx5/2 = 15/4`

Answer 3

`x : z = 15:4`

Explanation:

Before you can compare all three values in one ratio,
make `y` the same in both ratios:

`x" ":" "y" ":" " z`

`5" ":" "2" ":" " z`
`color(red)(15" ":" "6)" ":" " z`

`x" ":" "3" ":" " 2`
`x" ":" "color(red)(6" ":" " 4)`
`color(red)(15" ":" "6)" ":" " z`

Now that we have `y` the same in both ratios:

`color(red)(15" ":" "6" ":" " 4)`

`:. x : z = 15:4`