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

3 Answers
Mar 23, 2016

#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#

Nov 18, 2016

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#

Nov 18, 2016

# 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#