If a mother is 5x her daughters age and when the daughter is her mom's current age the sum of their ages will be 126.

Question

Solve for the daughter's current age

Answer 1

Let x be the daughter's age and y be the mother's age.  We have two unknowns (x and y), so we need two equations relating x and y to solve the problem.

 

The mother is 5 times her daughter's age:

 

y = 5x

 

When the daughter is her mom's current age (y), the sum of their ages will be 126.  The daughter will be her mom's present age in y-x years.  So when the daughter is y years old, her mom will be y+y-x = 2y - x years old:

 

y + 2y -x = 126

3y - x = 126

 

Since the first equation tells us that y = 5x, let's substitute 5x in place of y in the second equation and solve for x, the daughter's current age:

3y - x = 126

3(5x) - x = 126        [substituted 5x in place of y]

15x - x = 126

14x = 126

x = 9    --->  The daughter is 9 years old

 

Solve for y, the Mom's current age:

y = 5x                     [First equation]

y = 5(9)                  [ x = 9 ]

y = 45

 

Check:

3y - x = 126           [Second equation]

3(45) - 9 = 126      [Plug in x=9 and y=45]

135 - 9 = 126

126 = 126             CHECK!