If `10` be added to four times a certain number, the result is `5` less than five times the number. Find the number.

Options

A. `25`
B. `15`
C. `16`
D. `18`

Answer

To solve the problem step by step, we will first define the variable and then set up the equation based on the information given in the question.

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Set up the equation
According to the question, if 10 is added to four times the number, we can express this as:
\[ 4x + 10 \]

The question also states that this result is equal to 5 less than five times the number. We can express this as:
\[ 5x - 5 \]

Now we can set up the equation:
\[ 4x + 10 = 5x - 5 \]

### Step 3: Rearrange the equation
To solve for \( x \), we will rearrange the equation. First, we will move all terms involving \( x \) to one side and constant terms to the other side. We can subtract \( 4x \) from both sides:
\[ 10 = 5x - 4x - 5 \]

This simplifies to:
\[ 10 = x - 5 \]

### Step 4: Solve for \( x \)
Next, we will isolate \( x \) by adding 5 to both sides:
\[ 10 + 5 = x \]
\[ 15 = x \]

### Step 5: Conclusion
Thus, the number is:
\[ x = 15 \]

### Final Answer
The required number is **15**.

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