Given Data:
A and B are friends, and their ages differ by 2 years: A - B = 2
A's father D is twice as old as A: D = 2A
B is twice as old as his sister C: B = 2C
The age of D and C differ by 40 years: D - C = 40
Equations:
A - B = 2
D = 2A
B = 2C
D - C = 40
Solutions:
Using the given data, let's solve the system of equations:
Substitute equation 2 into equation 4:
2A - C = 40
Substitute equation 3 into equation 1:
A - 2C = 2
Now, we have a system of two equations:
2A - C = 40
A - 2C = 2
Solving these equations using elimination or substitution method:
Multiply equation 2 by 2:
2(A - 2C) = 2(2)
2A - 4C = 4
Now, subtract equation 1 from the above equation:
(2A - 4C) - (2A - C) = 4 - 40
2A - 4C - 2A + C = -36
-3C = -36
Divide both sides by -3:
C = -36 / -3
C = 12
Substitute the value of C back into equation 1:
A - 2(12) = 2
A - 24 = 2
A = 2 + 24
A = 26
Substitute the value of A into equation 3:
B = 2C
B = 2(12)
B = 24
Answer:
The age of A is 26, and the age of B is 24.
