Let's translate the sentence into a mathematical equation step by step.
The sentence "Ten less than the quotient of a number and 4 is 6" can be broken down as follows:
1. "The quotient of a number and 4" means we are dividing a certain number by 4. If we let the number be represented by n, then this quotient can be written as n ÷ 4 or n/4.
2. "Ten less than" refers to subtracting 10 from something. So we have to take our quotient from the previous step and subtract 10 from it. This can be written as (n ÷ 4) - 10 or (n/4) - 10.
3. Finally, the sentence tells us that the result of subtracting 10 from the quotient of a number and 4 "is 6". In mathematics, the word "is" usually represents the equality sign (=). So, we equate our expression to 6, resulting in the equation:
(n ÷ 4) - 10 = 6.
Now let's match our equation to the given options:
A. n ÷ 4 + 10 = 6 (This option is incorrect because it adds 10 instead of subtracting 10.)
B. n · 4 = 10 = 6 (This option is incorrect for a couple of reasons. First, it seems to have a typographical error with two equality signs, and it suggests multiplying by 4 rather than dividing by 4.)
C. n ÷ 4 - 10 = 6 (This option correctly represents the information given in the sentence: "The quotient of a number and 4" as n ÷ 4, and "Ten less than" as - 10 added to the quotient, and then equating the entire expression to 6.)
Thus, the correct answer is Option C: n ÷ 4 - 10 = 6.