Blank Ratio?

Question

1:??:8 = 3:12:??

I got 12 for the first blank and 8 for the second, are these the correct answers?

Answer 1

A ratio of a:b:c has the characteristic that ax+bx+cx = total number of observations.
 
This is how ratios are reduced like fractions.  Thus, a ratio of 20:40:5 is the same as 4:10:1.
 
The ratio 3:12:?? has been reduced to 1:??:8, so it must have started as --

         1*3 : 4*3: 8*3        (3:12:24)
   and when it is reduced it becomes  1:4:8
 
To check -- make sure that  3:12:24 reduces to 1:4:8.

Answer 2

Ratios or proportions can be rewritten as fractions.  Let's look at the first pair...

 

Let ??=x

1:x=3:12

1/3=x/12...rewrite as a fraction

1(12)=3x...cross-multiply

12=3x

3x=12.......rewrite variable on LHS

  x=4........divide both sides by 3

 

So...

1:4=3:12

Note that the multiplier factor from the first ratio to the second ratio is 3...

1x3=3

4x3=12

 

Now try the second ratio...

1:3=8:x

1/8=3/x

...complete by cross-multiplication, solve for "x".  What is the multiplier?