Write and solve an equation: Find a number such that the difference of 97 and eighteen times the number is five times one more than the number

1. Let the number be x .
2. According to the problem, the difference of 97 and eighteen times the number ( 18x ) is equal to five times one more than the number ( 5(x+1) ).

The equation can be written as:
97 - 18x = 5(x + 1)

3. Expand the term on the right-hand side:
5(x + 1) = 5x + 5

4. Substitute back into the equation:
97 - 18x = 5x + 5

5. Bring all terms involving x to one side and constant terms to the other:
97 - 5 = 18x + 5x

6. Simplify both sides:
92 = 23x

7. Solve for x :
x = \frac{92}{23} = 4

Therefore, the number is x = 4 .