Age Problem Setup

Let the present age of A be $A$ years and the present age of B be $B$ years.

From the first statement, "A is 6 years older than B":

$ A = B + 6 \quad \quad (1) $

From the second statement, "10 years ago":

• A's age was $A - 10$ years.
• B's age was $B - 10$ years.

The condition is "B's age was three quarters of A's age":

$ B - 10 = \frac{3}{4}(A - 10) \quad \quad (2) $

Solving for A's Age

Substitute $B$ from equation (1) into equation (2). From (1), we get $B = A - 6$.

Substitute $B = A - 6$ into equation (2):

$ (A - 6) - 10 = \frac{3}{4}(A - 10) $

Simplify the equation:

$ A - 16 = \frac{3}{4}(A - 10) $

Multiply both sides by 4 to eliminate the fraction:

$ 4(A - 16) = 3(A - 10) $

Expand both sides:

$ 4A - 64 = 3A - 30 $

Rearrange the terms to solve for $A$:

$ 4A - 3A = 64 - 30 $

$ A = 34 $

Conclusion

The present age of A is 34 years.