Question

In 4 years, a mother will be 5 times as old as her daughter. At present, the mother is 9 times as old as the daughter. How old are the mother and the daughter today.

Answer 1

Set up a system of equations:

y + 4 = 5(x + 4)
y = 9x

Where 'y' represents the mother's age and 'x' represents the daughter's age.

Plug in 9x for 'y' in the first equation:

y + 4 = 5(x + 4)

9x + 4 = 5(x + 4)

Distribute 5 into the parenthesis:

9x + 4 = 5x + 20

Subtract 5x to both sides:

4x + 4 = 20

Subtract 4 to both sides:

4x = 16

Divide 4 to both sides:

x = 4

Plug this into any of the two equations to find 'y':

y = 9x

y = 9(4)

Multiply:

y = 36

So at the present, the daughter is 4 years old and the mother is 36 years old.

Answer 2

4 mother will be 5 times as old as her daughter.
Mother= 9 times as old as the daughter.
4 times 5= 20 mother
9 times 5= 45
Mother=29
daughter=15