The mother is twice as old as her daughter. The daughter is 6 years younger than her uncle. The sum of their ages was 87 years five years ago. What are their present ages?

Let $M$ be the mother's present age.
Let $D$ be the daughter's present age.
Let $U$ be the uncle's present age.

From the first statement, "The mother is twice as old as her daughter":

From the second statement, "The daughter is 6 years younger than her uncle":

This can be rewritten as:

From the third statement, "The sum of their ages was 87 years five years ago":
Five years ago, their ages were $M-5$, $D-5$, and $U-5$.

Substitute Equation 1 ($M=2D$) and Equation 2 ($U=D+6$) into Equation 3:

Combine like terms:

Subtract 6 from both sides:

Divide by 4 to find the daughter's present age:

The daughter's present age is 24 years.

Using Equation 1 to find the mother's age:

The mother's present age is 48 years.

Using Equation 2 to find the uncle's age:

The uncle's present age is 30 years.

The present ages are:

• Mother: $\boxed{\text{48 years old}}$
• Daughter: $\boxed{\text{24 years old}}$
• Uncle: $\boxed{\text{30 years old}}$