Chapter 1.5, Problem 15IP

To determine

How old are Brianne and Camila now.

Answer to Problem 15IP

  $\begin{array}{l}\text{Brianne is 12 years old}\\ \text{Camila is 4 years old}\end{array}$

Explanation of Solution

Given :

Brianne is three times as old as Camila. Four years from now she will be just two times as old as Camila.

In order to find how old are Brianne and Camila now, first let b is the present age of Brianne and c is the present age of Camila now write the equation for each statement, that is ‘Brianne is three times as old as Camila’ so the equation is

  $b=3c\text{equation1}$

Second statement ‘four years from now she will be just two times as old as Camila’ so the eqation is

  $b+4=2\left(c+4\right)\text{equation 2}$

Solving equation 2, first multiply 2 inside the bracket and then subtract 4 from both sides as shown below:

  $\begin{array}{l}b+4=2\left(c+4\right)\text{equation 2}\\ b+4=2c+8\\ b+4-4=2c+8-4\\ b=2c+4\end{array}$

Now, putting $b=3c$ from equation 1

  $\begin{array}{l}b=2c+4\\ 3c=2c+4\\ 3c-2c=2c-2c+4\\ c=4\end{array}$

So, Camila is 4 years old, to find the age of Brianne putting c=4 in equation 1

  $\begin{array}{l}b=3c\\ b=3\times 4\\ b=12\end{array}$

So, Brianne is 12 years old.