Ages of Marco and Lia

Statement

Marco is three times as old as Lia. In $8$ years Marco will be twice as old as Lia. How old are they?

Solution

Unknown. $x=$ Lia’s age today. Marco today is $3x$.

Equation. In $8$ years Marco will be $3x+8$ and Lia $x+8$. The condition “Marco twice Lia” gives: $3x+8 = 2(x+8) \implies 3x+8=2x+16 \implies x=\boxed{8}$ Lia is $8$ years old, Marco $24$. Check: in $8$ years they will be $16$ and $32$, and indeed $32=2\cdot 16$.

Links

Topics: First-degree equations
Concepts: Equation · Unknown
Methods: Age problem
Skills: Modelling · Solving equations
Exercise type: Word problem