a mother is 24 years,older than her daughter . If the daughters age is x years.(a) express the mothers age in terms of x.(b) find x when the daughters age is 1/3 of her mothers age.
(a) The mother's age can be expressed as x + 24 years.
(b) We can set up the equation:
x = (1/3)(x + 24)
Multiplying both sides by 3, we get:
3x = x + 24
Subtracting x from both sides, we get:
2x = 24
Dividing both sides by 2, we get:
x = 12
Therefore, when the daughter's age is 1/3 of her mother's age, the daughter is 12 years old and the mother is 36 years old.
(a) To express the mother's age in terms of x, we can use the information given that the mother is 24 years older than her daughter.
So, the mother's age would be x + 24.
(b) To find x when the daughter's age is 1/3 of her mother's age, we can set up an equation.
Let x be the daughter's age. The mother's age would be 3 times the daughter's age, as stated in the question.
Therefore, 3x = x + 24.
Simplifying the equation, we have:
3x - x = 24.
2x = 24.
Dividing both sides of the equation by 2:
x = 12.
So, when the daughter's age is 1/3 of her mother's age, her age is 12 years.