Guide 4 (fourth edition) page 58

[bsolpietro]

I understand the method used to combine the ratio in the text, or at least I think I do, but what if I alter the example a bit - how would I solve?

Example given
C:A:L_______________________C:A:L
3:2: ________Multiply by 5____15:10:
5:_:__:4_____Multiply by 3____15:__:12

This is the combined ratio:15:10:12

My example
C:A:B:L_____________________C:A:B:L
3:2:_:_______Multiply by ?
5:_:_:4______Multiply by ?
_:4:1:_______Multiply by ?

Thanks in advance. (please try and visualize w/out the underlines - used to edit spacing)

[michael.a.gabe]

3:2:_:_______Multiply by ?
5:_:_:4______Multiply by ?
_:4:1:_______Multiply by ?

1) Prudence would dictate multiplying first 2 rows to get the 3 & 5 to their LCM of 15.

15:10:__:__
15:__:__:12
__:4:1__

So now you can combine the top 2 rows and get the following:
15:10:__:12
__:4:1___

2) The 2nd column of 10 & 4 can be shown in their LCM of 20 by multiplying by 2 & 5, respecitvely of course.
30:20:__:24
__:20:5:__

Combine the 2 lines:
30:20:5:24

Don't feel bad, it took me about 20 minutes.

[Ben Ku]

(a) 3:2:_:_______Multiply by ?
(b) 5:_:_:4______Multiply by ?
(c) _:4:1:_______Multiply by ?

I would use ratios (a) and (c), since there is a common multiple in the second slot.

Multiplying ratio (a) by 2, we get
(d) 6 : 4 : 1 : _

We can combine (d) with (b) by multiplying (d) by 5 and multiplying (b) by 6. This way, the first slot can be 30.
(d) 30 : 20 : 5 : _
(b) 30 : _ : _ : 24

The four terms are in the following ratio:
30 : 20 : 5 : 24

Hope that makes sense,