Question

The sum of two numbers is 30 and their quotient is 2

Answer 1

Let x, and y be the two numbers the problem is asking for, then we can set the following system of equations:

$\begin{gathered} x+y=30, \\ \frac{x}{y}=2. \end{gathered}$

Solving the second equation for x, we get:

$\begin{gathered} \frac{x}{y}\cdot y=2\cdot y, \\ x=2y\text{.} \end{gathered}$

Now, substituting x=2y in the first equation we get:

$2y+y=30.$

Solving for y we get:

$\begin{gathered} 3y=30, \\ \frac{3y}{3}=\frac{30}{3}, \\ y=10. \end{gathered}$

Finally, we substitute y=10 in the first equation on the board and get:

$x+10=30.$

Solving for x we get:

$\begin{gathered} x=30-10, \\ x=20. \end{gathered}$

Answer: the numbers we are looking for are 20 and 10.