Question

The difference between two numbers is $26$ and one number is three times the other. Find them?

Answer 1

Step 1. Determine the equations.

Assume that the numbers are $x\mathrm{and}y$.

The difference between the numbers is $26$.

So, the equation obtained is $x-y=26$.

The bigger number is $3$ times the smaller number.

So, the other equation obtained is $x=3y$.

Step 2. Solve the obtained equation

Substitute $x=3y$ into $x-y=26$ and solve for $y$:

$\begin{array}{rcl}3y-y& =& 26\\ & \Rightarrow & 2y=26\\ & \Rightarrow & y=13\end{array}$

Substitute $y=13$ into $x-y=26$ and solve for $x$:

$\begin{array}{rcl}x-13& =& 26\\ & \Rightarrow & x=39\end{array}$

So, the numbers are $39\mathrm{and}13$.