Anne is 3/4 as old as Judy. Four years ago Anne was 2/3 as old as Judy. How old are they

Question

There are no other detials that are given for this question 

Answer 1

Hello John

 

the trick to this problem is the Four years age. let Judy be x years old four years ago, now Judy  was x+4 years old

 

if Anne was y  years old four years ago then,

 

y = (2/3)x four years ago, she is y = (3/4)(x + 4) now 

 

y = 2x/3   and

 

y =3x/4 - 3,   plug in for y,

 

2x/3 = 3x/4 - 3  the common factor for  3 and 4 is 12, i.e. 3*4 = 12

 

(2x/3)*12 =(3x/4)*12 - 3*12

8x             = 9x - 32

8x - 9x = -32

        -x = -32

       x = 32 

 

At the present x + 4 = 32 + 4 = 36 and y = 3x/4 - 3 = 3*32/4 -3 = 21

 

Now Judy is 36  and Anne is 21 years old.