Answer to Question #5802 in Algebra for Danial Aziz

Question

The age of mother is four times her daughter age, after five years the sum of their ages will be 60, find their ages now?

Answer 1

Let x – age of mother, y – age of daughter
The age of mother is 4 times her daughter age: we have the first equation x = 4y
After 5 years the sum of their ages will be 60: in 5 year the age of mother will be (x+5), the age of daughter will be (y+5), we have the second equation (x+5)+(y+5) = 60
So, we have the system of equations:
x = 4y
x+y+10 = 60
(from the 2nd equation x = 50 – y, put it in the 1st one: 4y = 50 – y, y = 10, x = 4y = 40)
The roots: x = 40, y = 10
The answer: now mother’s age is 40 years old, daughter’s age is 10 years old