Age problem

Question

One day the absent minded professor asked his wife"How old are our daughters?",the wife replied," I cant remember dear. but i do seem to to recall that if Bertha's age is 10 years younger than , she'd be 1/4 of Ann's present age. If Ann is 12 years older she'd be twice Bertha's age.". what is the age of the girls?  

Answer 1

let B= Bertha's age

let A=Ann's age

B-10=(1/4)A

A+12=2B

A=2B-12

substitute

B-10=(1/4)(2B-12)

B-10=(1/2)B-3

B-(1/2)B=10-3

(1/2)B=7

B=14

14-10=(1/4)A

4=(1/4)A

16=A

Anna is 16 years old and Bertha is 14 years old