Question

Points B and C lie on line AD. Find AC if AB/BD =3/4, AC/CD=5/6,and BD =66

Answer 1

BD = 66
AB:BD = 3:4
⇒ AB = (3/4)∙BD
= (3/4)∙66
= 49.5

AD = AB + BD
= 115.5

AC:CD = 5:6
⇒ AC = (5/11)∙AD
= 52.5

Answer 2

first find the legnt of the line then find the

so ratios are
AB:BD=3:4
AC:CD=5:6

BD=66

subsitute
AB:66=3:4
so we know that 4 units represent 66 so divide 66 by 4
66/4=16.5

so multiply by 3 to find AB
AB=3 times 16.5=49.5
66+49.5=115.5

therfor
AC+CD=115.5
5:6
5+6=11
11 units
115.5/11=1 unit
10.5
AC:CD=5:6

AC=5 units
10.5 times 5=52.5

AC=52.5