Question

If A:B = 7:8 an B:C =12:7,find A:C in its simplest form.

Answer 1

84:56

Explanation:

a:b:c

(7:8)

( 12:7)

Answer 2

A:C = 3:2

Explanation:

A:B = 7:8 is a proportion relationship and can be represented using fractions:

`\displaystyle{(A)/(B) = (7)/(8)}`

Similarly the proportion relation B:C = 12:7 can be represented as:

`\displaystyle{(B)/(C) = (12)/(7)}`

Multiply the first equation by the second

`\displaystyle(A)/(B)\;\mathsf{x}\;(B)/(C) = (7)/(8)\;\mathsf{x}\;(12)/(7)`

This evaluates to

`\displaystyle(A)/(C) = (12)/(8)`

Simplifying gives us

`\displaystyle(A)/(C) = (3)/(2)`

So A:C = 3: 2