Final Answer:
The inequality representing the situation is x/15 ≤ 450, where x is the number.
Step-by-step explanation:
To express the given situation as an inequality, we use the phrase ""the quotient of a number and 15 is no greater than 450."" The quotient in this case is x/15, where x represents the number. The phrase ""no greater than"" is represented by the inequality symbol ≤, resulting in the inequality x/15 ≤ 450.
Breaking down the inequality, x/15 ≤ 450 means that when the number x is divided by 15, the result is less than or equal to 450. In other words, the number divided by 15 should not exceed 450. To visualize this, consider that if the number were to be 450, the quotient x/15 would be exactly 30. Any number less than 450 would result in a quotient less than 30, satisfying the inequality.
In conclusion, the inequality x/15 ≤ 450 effectively represents the given situation, ensuring that the quotient of the number and 15 does not exceed 450. This provides a clear mathematical expression of the constraint imposed by the situation, allowing for easy interpretation and solution.