Finding a ratio?

Question

AB:BC = 2:3 therefore, AB:AC= 2:5

Can someone explained how the ratio of 2:5 is determined only from the ratio of AB:BC?

Thank You,

Brian

Answer 1

Hi Brian!

This problem requires that all points be on a single line (we call them "colinear" points). AB represents the distance from point A to point B, and BC represents the distance from point B to point C. Like so:

|--AB----|-----BC-------|

A--------B---------------C

So if AB:BC = 2:3 we have the situation where:

|----2----|-------3--------|

A--------B---------------C

How does AB relate to AC in this situation? Try to come up with an answer on your own before continuing to read.

The value we give to AB is arbitrary since all we want is the ratio, however, it is easiest to pick AB to be 2 so it matches the numbers we were already given. If AB is 2, then BC is still 3 and AC is the distance AB + BC, which in this case is 2 + 3 = 5.

|----2----|-------3--------|

A--------B---------------C

|-----------5---------------|

That gets us to AB:AC = 2:5. Hope this helps!

-Nathan

Answer 2

Brian --

This problem assumes that AB + BC = AC...which is not entirely clear in the problem.

AB/BC = 2/3

3AB = 2BC => BC = (3/2)AB

Substitute

AB + (3/2)AB = AC

2AB + 3AB = 2AC

5AB = 2AC

(AB/AC) = 2/5