Solve for X: Mother is 25 Years Older and Ages Sum to 40

To solve this problem, we need to set up a system of equations based on the information given. We can start by assigning variables to represent the ages of the mother and daughter:
$M$ for the mother's age, and $D$ for the daughter's age.

From the problem statement, we know the following:

• The mother is 25 years older than her daughter: $M = D + 25$.
• The sum of their ages is 40: $M + D = 40$.

We can substitute the first equation into the second equation to solve for $D$:

$(D + 25) + D = 40$

This simplifies to:

$2D + 25 = 40$

Subtract 25 from both sides to isolate the term with $D$:

$2D + 25 - 25 = 40 - 25$

Which is:

$2D = 15$

Now, divide both sides by 2 to solve for $D$:

$D = \frac{15}{2}$

Thus, the daughter's age is $7.5$ years old.

This solution checks out as it satisfies both given conditions in the problem statement.