Final answer:
The unknown number can be found by setting up an algebraic equation based on the provided relationships between 108, 72, and the number. After cross-multiplying and simplifying, the solution comes down to testing the options given, which reveals that the correct answer is 18.
Step-by-step explanation:
The question asks for a solution to an algebraic problem where a number is sought based on given relationships described by rational expressions. To find the number, let's denote the unknown number as n. According to the problem, dividing 108 by n plus some unspecified amount results in the same as dividing 72 by n minus 3.
Setting up the equation gives us 108 / (n + x) = 72 / (n - 3), where 'x' represents the unspecified 'more than' amount. Since we cannot determine 'x', we should be focusing on just the known variables and constants. Solving for n requires manipulation of the rational expressions. We can multiply both sides by (n + x) and by (n - 3) to eliminate the denominators, and then solve for n by looking at the possible options provided.
After cross-multiplying and simplifying, the resulting equation would be of the form (108 * (n - 3)) = (72 * (n + x)), leading to a linear equation in n. Testing each option given in the multiple choices and considering that they should result in the same quotient, the correct answer can be deduced. For example, for n = 18: 108 / (18 + x) = 72 / (18 - 3) or 108 / (18 + x) = 72 / 15, which simplifies to 108 / (18 + x) = 4.8. Here, we can see that adding any positive number to 18 in the denominator would reduce the fraction further from 4.8, indicating that 18 + x must equal 18, hence x equals 0 and n is indeed 18.