[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- Revathi's age is 1/3 of her mother's age. If their difference in age is 24 years, find Revathi's age.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
Given,
- Mother's age = x
- Revathi's age = 1/3 x = ?
- Difference in their age = 24 years ⇨ x - 1/3 x = 24.
Now, let's solve this question using the above equation which we just formed.
[tex] \sf \: x - \frac{1}{3}x = 24 \\ [/tex]
Combine x and [tex]\sf\:-\frac{1}{3}x [/tex] to get [tex]\sf\frac{2}{3}x[/tex].
[tex] \sf\frac{2}{3}x=24 \\ [/tex]
Multiply both sides by [tex]\sf\frac{3}{2}[/tex], the reciprocal of [tex]\sf\frac{2}{3}[/tex].
[tex] \sf \: x=24\times \left(\frac{3}{2}\right) [/tex]
Express [tex]\sf24\times \left(\frac{3}{2}\right)[/tex] as a single fraction.
[tex] \sf \: x=\frac{24\times 3}{2} \\ [/tex]
Multiply 24 and 3 to get 72.
[tex] \sf \: x=\frac{72}{2} \\ [/tex]
Divide 72 by 2 to get 36.
[tex] \boxed{ \bf \: x=36 }[/tex]
We now have the age of Revathi's mother (x) = 36 years. Now, let's find Revathi's age ⇨ [tex]\sf\:(\frac{1}{3}x) [/tex]
[tex] \rightarrow \sf \: \frac{1}{3} x \\ \rightarrow \sf \: \frac{1}{3} \times 36 \\ \rightarrow \sf \: \frac{1}{ \bcancel 3} \times \bcancel{36} \\ \rightarrow \sf \:1 \times 12 \\ = \boxed{\boxed{\bf \: 12}}[/tex]
- So, Revathi is 12 years old.
