Question

Lina is three times as old as Paul. If the sum of their ages is 48, find their respective ages.

• A. Age of Paul is 22.5 years and age of Lina is 25.5 years.
• B. Age of Paul is 12 years and age of Lina is 36 years.
• C. Age of Paul is 36 years and age of Lina is 12 years.

Answer 1

The correct option is B Age of Paul is 12 years and age of Lina is 36 years.

Let Paul's age be $x$ years.

Lina is 3 times as old as Paul.
$\therefore$ Lina's age = $3\times x=3x\text{years}$

Algebraic expression of Lina's age is $3x$.

It is given that the sum of their age is 48.
$\therefore 3x+x=48$
$\Rightarrow 4x=48$

To undo the multiplication we divide the both side of the equation by $4$.
$4x=48$
$\Rightarrow \frac{4\times x}{4}=\frac{48}{4}$
$\Rightarrow x=12$

$\therefore$ Paul's age is 12 years.

$\Rightarrow \text{Lina's age}=3x=3\times 12=36\text{years}$

To verify this we add their ages and check if we get 48 as the sum.
$36+12=48$
Hence, the results are correct.