Question

The smaller of two numbers is 2 less than the larger. If 3 times the larger number is equal to 6 times the smaller, find the numbers.

Answer 1

Let x be the smaller number, y the larger one. With the information given, we got the following equations

$\begin{gathered} y-2=x \\ 3y=6x\rightarrow y=2x \end{gathered}$

We need to replace the second equation in the first one to get the solution

$\begin{gathered} y=2x\text{ and }y-2=x\text{ } \\ 2x-2=x\rightarrow \\ 2x-x=2 \\ x=2 \end{gathered}$

if x=2, we get that

$y=2x=2\cdot2=4$