Question

A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Answer 1

Hint: For solving this problem, we first let two numbers be x and y. Now to solve them we require two equations. By using the first part of the problem statement, we form the first equation as y = 5x. Similarly, from the second part we form another equation. By solving both the equations we get the numerical value of numbers.

Complete step-by-step answer:
For our problem, let one number be x and another number be y. From the first line of the problem statement vi form equation (1) as, $y=5x\ldots (1)$
Now adding 21 to both the numbers we get,
$y+21\text{ and }x+21$
Now using the second statement be form another equation (2) as, $y+21=2(x+21)\ldots (2)$
Since there are two variables, we formulated two equations so we can easily solve this problem. Putting the value of y from equation (1) to equation (2) we get,
$\begin{align}
  & 5x+21=2x+42 \\
 & 5x-2x=42-21 \\
 & 3x=21 \\
 & x=\dfrac{21}{3}=7 \\
 & y=5\times 7=35 \\
\end{align}$
Therefore, the first number is 5 and the second number is 35.

Note: The key step for solving this problem is the knowledge of interpretation of data into equations. Students must remember that the number of variables and number of equations must be the same for obtaining a solution.