Answer the Following:

Question

The sum of the ages of Shang and Agatha is 40 years. After 10 years Shang will be twice as old as Agatha. What is Shang's present age? What is Agatha's present age?

Answer 1

S = Shang's age in years

A = Agatha's age in years

Lets solve this by setting up some equations:

"sum of the ages of Shang and Agatha is 40 years"

S + A = 40

"After 10 years Shang will be twice as old as Agatha"

(S + 10) = 2 (A + 10)

(S + 10 and A + 10 represent their ages respectively in ten years. The factor of 2 on the left side represents that Shang will be twice as old as Agatha in this time.)

System of equations:

S + A = 40

(S + 10) = 2 (A + 10)

Solve by substitution:

S + A = 40

S = 40 - A

((40 - A) + 10) = 2(A + 10)

50 - A = 2A + 20

-3A = -30

A = 10

S + 10 = 40

S = 30