Question 1141879
let a represent the age of the older sister.
let b represent the age of the younger sister.


the ratio of the older sister to the younger sister is 4:3.


you get a/b = 4/3


the older sister is 3 years older than the younger sister.


you get a = b + 3


in the equation of a/b = 4/3, replace a with b + 3 to get:


(b + 3) / b = 4 / 3


multiply both sides of this equation by b to get b + 3 = 4 * b / 3


multiply both sides of this equation by 3 to get 3 * b + 9 = 4 * b


subtract 3 * b from both sides of this equation to get 9 = 4 * b - 3 * b


combine like terms to get 9 = b.


that's the age of the younger sister.


the older sister is 3 years older, so the age of the older sister is 12.


you have a = 12 and b = 9, with a representing the age of the older sister and b representing the age of the younger sister.


the ratio of the age of the older sister to the age of the younger sister is equal to a / b which is equal to 12 / 9.


this can be simplified to 4 / 3, confirming the solution is good.