Question

The difference between two numbers is 22. The sum of twice the smaller number and 3 times the greater number is 246.

Answer 1

Given:

The difference between two numbers is 22.

The sum of twice the smaller number and 3 times the greater number is 246.

Required:

To find the two numbers.

Explanation:

Let the two numbers be x and y.

Let y be the smaller number.

The difference between two numbers is 22.

$x-y=22$

The sum of twice the smaller number and 3 times the greater number is 246.

$2y+3x=246$

Now

$\begin{gathered} 2y+3(22+y)=246 \\ 2y+66+3y=246 \\ 5y=246-66 \\ 5y=180 \\ y=\frac{180}{5} \\ y=36 \end{gathered}$

Now x is,

$\begin{gathered} x-36=22 \\ x=22+36 \\ x=58 \end{gathered}$

Final Answer:

The two numbers are 58 and 36.