Question

Kamal is $17$ years older that Gina. Gina is $3$ years younger than Rachelle. If the sum of their ages is $77$, how old is Gina?

Answer 1

Find the age of Gina:

Let the ages of Kamal, Gina, and Rachelle be $k,g\text{and}r$ years respectively.

$\because$The sum of ages is $77$.

$\Rightarrow k+g+r=77$ ..$\left(1\right)$

And, Kamal is $17$ years older than Gina.

$\Rightarrow k=g+17$ ….$\left(2\right)$

Using the equation $\left(2\right)$ in the equation $\left(1\right)$:

$\begin{array}{rcl}k+g+r& =& 77\\ & \Rightarrow & g+17+g+r=77\\ & \Rightarrow & 2g+r=60....\left(3\right)\end{array}$

Now, Gina is $3$ years younger than Rachelle:

$\begin{array}{rcl}& \Rightarrow & g=r-3\\ & \Rightarrow & r=g+3\dots .\left(4\right)\end{array}$

Using the equation $\left(4\right)$ in the equation $\left(3\right)$:

$\begin{array}{rcl}2g+r& =& 60\\ & \Rightarrow & 2g+\left(g+3\right)=60\\ & \Rightarrow & 3g+3=60\\ & \Rightarrow & 3g=57\\ & \Rightarrow & g=19\end{array}$

Hence, the age of Gina is$\mathbf{19}$ years old.