Question

Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get $36$. How old is each sister? (a) Write an equation that represents the situation. Explain any variable used. (b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.

Answer 1

Step-1: Finding an equation that represent the situation:
Let the Kim's age be $y$ and her sister's age be $x$
Kim's age is twice that of her sister, So $y=2x...\left(i\right)$
Adding Kim's age to her sister's age, we get $36$
$x+y=36...\left(ii\right)$

Step-2: Finding the age of Kim and her sister:

Putting equation $\left(i\right)$ in equation $\left(ii\right)$, we get
$$\begin{gathered} \Rightarrow x+y=36 \\ \Rightarrow x+2x=36\mathbf{}\mathbf{[}\mathbf{\because }\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{}\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{(}\mathit{i}\mathbf{\left)}\mathbf{\right]} \\ \Rightarrow 3x=36 \\ \Rightarrow x=\frac{36}{3} \\ =12\mathrm{years} \end{gathered}$$

Kim's age$=2\times 12$
$=24\mathrm{years}$

Hence, age of Kim and her sister is $\mathbf{24}\mathbf{}\mathbf{years}\mathbf{}\mathbf{\&}\mathbf{}\mathbf{12}\mathbf{}\mathbf{years}$.