Let s be the son’s current age and d be the daughter’s current age. The system of equations is:
s - 10 = 2(d - 10)
s = 3 + d
Since s is already set to an equation, we can use the substitution method for s in the other equation:
s = 3 + d
s - 10 = 2(d - 10)
3 + d - 10 = 2(d - 10)
Simplify and solve for d:
3 + d - 10 = 2(d - 10)
-7 + d = 2d - 20
-7 = d - 20
13 = d
The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:
s = 3 + d
s = 3 + 13
s = 16
The son is 16 years old. Let us use the other equation to check our solutions:
s - 10 = 2(d - 10)
16 - 10 = 2(13 - 10)
6 = 2(3)
6 = 6
It checks out. The son is 16 years old, and the daughter is 13 years old.
