Question

Given that one number is three times the other number. If 15 is added to both the numbers, then one of the numbers is twice the other new number. Find the numbers.

Answer 1

Hint: Assume unknown quantity denoted by x or y or a or b (x, y, z, a, b, c all are variables).
The unknown variable must be represented in small alphabets.
Form the mathematical equations as stated in the language of question.
The word ‘twice’ implies the multiplication by ‘2’, similarly, ‘two times’ also implies multiplication by ‘2’.

Complete step by step solution:
Step 1
Let the one number \[ = x\]

Step 2
Let the another number $ = y$

Step 3
One number is three times the another number:
                                   $x = 3y$ …… (1)

Step 4
15 is added to both numbers (one and the other numbers):
                            $\therefore $ One number $ = x + 15$
                           Another number $ = y + 15$

Step 5
We know, $x > y$ (from (1))
                                                                                                                      …… (2)

Step 6
One of the number is twice the other new number:
 $x + 15 = 2(y + 15)$ (from (2))
$ \Rightarrow x + 15 = 2y + 30$
$ \Rightarrow 3y + 15 = 2y + 30$ (from (1))
$ \Rightarrow 3y - 2y = 30 - 15$
$ \Rightarrow y = 15$ …… (3)
$x = 3y = 3 \times 15$ (from (3))
    $ = 45$

Therefore, The one number is x = 45 and another number is y = 15.

Additional information:
The change in mathematical operator $(' + ',{\rm{ }}' - ',{\rm{ }}' \times ',{\rm{ }}' \div ')$takes place in an equation when numbers are transferred from one side to the other side of the equation.
The operator $ + \to - $ and vice versa, the operator $ \times \to \div $and vice versa.

Note:
Similar patterns should be followed in the questions of one unknown variable and/or more variables.
In question language ‘more than’ indicates addition to the latter sentence and ‘less than’ indicates subtraction from the latter sentence.