The Correct Answer and Explanation is:
Of course. Based on the provided image, the question is number 10.
The correct answer is C: 80/x – 10
Here is a detailed explanation of how to arrive at this answer.
To solve this problem, you must translate the verbal phrase “10 less than the quotient of 80 and a number x” into a mathematical expression. The most effective way to do this is to break the phrase down into smaller, more manageable parts.
First, let’s identify the core operation. The phrase contains “the quotient of 80 and a number x”. The word “quotient” signifies the result of a division. In mathematics, when you see “the quotient of A and B”, it means A is divided by B, which can be written as A ÷ B or, more commonly in algebra, as the fraction A/B. In this specific case, A is 80 and B is “a number x”. Therefore, this part of the phrase translates to 80/x.
Next, we must address the first part of the phrase, “10 less than”. This is a common phrase in algebraic translation that often causes confusion. It indicates subtraction. However, the order is very important. “10 less than” a certain value means you start with that value and then subtract 10 from it. For example, “10 less than 25” is calculated as 25 – 10, which equals 15. The phrase essentially reverses the order of the terms as they appear in the sentence.
Now, we can combine the two parts. We are asked to find “10 less than” the expression we already identified, which is 80/x. Following the rule we just established, we take the expression 80/x and subtract 10 from it.
This gives us the final algebraic expression: 80/x – 10.
This matches option C perfectly. Option A, 10 – 80/x, is incorrect because it subtracts the quotient from 10, not the other way around. Option B uses addition, which would correspond to “10 more than”. Option D uses incorrect operations entirely.
