two years ago the sum of a mothers age and her daughters was 56 . now, the mothers age is twice the daughters age.Find the present age of the mother and daughter
Now:
daughter ---- x
mother ------ 2x
2 years ago:
daughter = x-2
mother = 2x-2
x-2 + 2x-2 = 56
solve for x
Today:
Daughter's age = X years.
Mother's age = 2X years.
x + 2x = 56 + 2 + 2. Each is 2 years older.
To find the present age of the mother and daughter, we can use algebraic equations. Let's assume the daughter's age is x years.
According to the given information, two years ago, the sum of the mother's age and her daughter's age was 56. This can be written as:
(Mother's age two years ago) + (Daughter's age two years ago) = 56
The mother's age two years ago would be (2 years ago - x years ago), which simplifies to (2 - x) years ago. And the daughter's age two years ago would be (2 years ago - 0 years ago), which simplifies to 2 years ago.
So, the equation becomes:
(Mother's age two years ago) + (Daughter's age two years ago) = 56
(2 - x) + 2 = 56
4 - x = 56
-x = 56 - 4
-x = 52
x = -52 (This is an invalid age for the daughter)
Since the daughter's age cannot be negative, we made an error in our calculations or assumption.
Let's rephrase the problem:
Now, the mother's age is twice the daughter's age. This can be written as:
Mother's age = 2 * Daughter's age
If we use similar algebraic representation, let's assume the daughter's age is x years.
The equation becomes:
Mother's age = 2 * Daughter's age
M = 2x
The sum of their present ages should be 56. So we can set up another equation:
Mother's age + Daughter's age = 56
M + D = 56
Now we have a system of equations to solve simultaneously:
M = 2x
M + D = 56
To solve this system, we can use substitution or elimination method. Let's use substitution:
Substitute the value of M from the first equation into the second equation:
2x + D = 56
Now we have a single-variable equation:
2x + D = 56
But we still need another equation to solve for two variables (x and D). Unfortunately, the information given doesn't provide us with another equation. Therefore, we can't determine the specific present ages of the mother and daughter based on the given information.