A:B = 6:7 and B:C = 8:9, find A:B:C. I know that the answer, 48:56:63 is obtained, but I don't get why it is done the way it is done (by multiplying the terms of the ratio in some particular way). In what method is the answer obtained and why so?

Question

A:B = 6:7 and B:C = 8:9, find  A:B:C. I know that the answer, 48:56:63 is obtained, but I don't get why it is done the way it is done (by multiplying the terms of the ratio in some particular way). In what method is the answer obtained and why so?

directrix · Answer

A/B = 6/7 so cross multiplying gives 7A = 6 B.  B = (7/6) A.

directrix · Answer

B/C = 8/9 so 8C = 9B and C = (9/8) B.

But B = (7/6)A so back substituting, C = (9/8) B = (9/8) ((7/6) A.

directrix · Answer

C = (9/8) B = (9/8) ((7/6) A =( 63/48) A

A: B : C is now A : (7/6) A : ( 63/48) A

The A factors divide out yielding:

1 : 7/6  :  63/48

---------------

B = (7/6) A.

directrix · Answer

Multiply through by 48

48 : 56  : 63 for the A:B:C

anonymous · Answer

You just need a common ratio between the A:B and B:C so you want the B's the same as they are common between the two, so you multiply the first ratio A:B by 8 and the B:C by 7.

then the B components of the ratios are the same and you can join them up