# Answer to Question #5802 in Algebra for Danial Aziz

Question #5802

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?

Expert's answer

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

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

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