Problem Breakdown: Finding the Original Number

This problem asks us to find an unknown original number based on a series of arithmetic operations performed on it. We are given the final result of these operations, which is 91.

Setting Up the Algebraic Equation

Let's represent the unknown original number with the variable x.

The problem states the following steps:

• First, "A number is subtracted from 4 times of it". Mathematically, this is represented as $4x - x$.
• Simplifying this expression gives $3x$. This is the 'number obtained' or the 'resultant'.
• Next, "the number obtained is added to its (the resultant’s) next number". This means we take the resultant ($3x$) and add the integer immediately following it, which is $(3x + 1)$.
• So, the operation becomes $3x + (3x + 1)$.
• The problem states that "this gives the answer as 91".

Therefore, the equation we need to solve is:

$3x + (3x + 1) = 91$

Step-by-Step Solution Calculation

Now, we will solve the equation $3x + (3x + 1) = 91$ step by step to find the value of $x$.

1. Combine like terms: We group the terms containing $x$ together on the left side of the equation. $$3x + 3x + 1 = 91$$ $$6x + 1 = 91$$
2. Isolate the term with x: To get the term $6x$ by itself, we subtract 1 from both sides of the equation. $$6x + 1 - 1 = 91 - 1$$ $$6x = 90$$
3. Solve for x: Finally, to find the value of $x$, we divide both sides of the equation by 6. $$\frac{6x}{6} = \frac{90}{6}$$ $$x = 15$$

The calculation shows that the original number is 15.

Verifying the Calculated Number

To ensure our answer is correct, let's verify it using the conditions given in the problem:

• The original number is $15$.
• Calculate 4 times the original number: $4 \times 15 = 60$.
• Subtract the original number from 4 times it: $60 - 15 = 45$. This is the 'resultant'.
• Find the resultant's next number: $45 + 1 = 46$.
• Add the resultant to its next number: $45 + 46 = 91$.

Since the final result is 91, which matches the value given in the question, our calculated original number of 15 is correct.