Answer: The difference in their ages is 13.
Step-by-step explanation: We shall start by assigning letters to represent the age of each one of them, that is the unknown variables. So, we shall call Rodney’s age r, and his sister’s age we shall call t. If the sum of Rodney and his sister’s age is 31, then we can write this as an expression,
r + t = 31
Also three times Rodney’s age can be written as 3 times r, or simply put, 3r. So five years less than three times Rodney’s age is equal to 3r - 5. Hence his sister’s age is equal to 3r - 5, or simply put,
t = 3r - 5
What we now have is a pair of simultaneous equations
r + t = 31 ————(1)
t = 3r - 5 ————(2)
We shall use the substitution method here. From equation (2), t = 3r - 5. So we shall substitute for the value of t into equation (1).
r + t = 31 now becomes
r + 3r - 5 = 31
4r - 5 = 31
Add 5 to both sides of the equation
4r -5 + 5 = 31 + 5
4r = 36
Divide both sides of the equation by 4
r = 9.
That means Rodney’s age is 9.
If from equation (1) r + t = 31, we can now insert the value of r in order to find t.
r + t = 31
9 + t = 31
Subtract 9 from both sides of the equation
t = 22.
That means his sister’s age is 22 while Rodney’s age is 9.
Therefore the difference in age between Rodney and his sister is
22 - 9 which equals 13.
