7 increased by one-fifth of a number is 8. Write the expression and find the number.

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Understand the problem
We need to express the statement "7 increased by one-fifth of a number is 8" in mathematical terms.

### Step 2: Define the variable
Let the unknown number be represented by \( x \).

### Step 3: Write the expression
According to the problem, one-fifth of the number \( x \) can be expressed as \( \frac{1}{5} \times x \). The phrase "7 increased by one-fifth of a number" translates to:
\[ 7 + \frac{1}{5}x = 8 \]

### Step 4: Set up the equation
Now we have the equation:
\[ 7 + \frac{1}{5}x = 8 \]

### Step 5: Isolate the variable
To isolate \( \frac{1}{5}x \), we need to move 7 to the other side of the equation. We do this by subtracting 7 from both sides:
\[ \frac{1}{5}x = 8 - 7 \]
\[ \frac{1}{5}x = 1 \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 5 (the reciprocal of \( \frac{1}{5} \)):
\[ x = 1 \times 5 \]
\[ x = 5 \]

### Step 7: Conclusion
The number we were looking for is \( 5 \).