Let's go through each equation given in the question and verify which one accurately represents the provided number sentence:
"The product of 10 and a number is 3 less than the number."
First, let's represent the problem statement algebraically:
Let [tex]\( n \)[/tex] be the number.
The product of 10 and a number = [tex]\( 10n \)[/tex]
This product is equal to:
3 less than the number [tex]\( \Rightarrow n - 3 \)[/tex]
So, the equation should be:
[tex]\[ 10n = n - 3 \][/tex]
Let's verify if this matches one of the given equations:
1. [tex]\(\frac{10}{n} = 3 - n\)[/tex]
2. [tex]\(10n = 3 - n\)[/tex]
3. [tex]\(10n = n - 3\)[/tex]
4. [tex]\(\frac{10}{n} = n - 3\)[/tex]
Now we'll check each option:
1. [tex]\(\frac{10}{n} = 3 - n\)[/tex]
This equation states that 10 divided by [tex]\( n \)[/tex] equals 3 minus [tex]\( n \)[/tex]. This does not match our algebraic representation, which involves multiplication of 10 and [tex]\( n \)[/tex].
2. [tex]\(10n = 3 - n\)[/tex]
This equation states that the product of 10 and [tex]\( n \)[/tex] equals 3 minus [tex]\( n \)[/tex], which does not match our algebraic representation either since our equation has [tex]\( n - 3 \)[/tex] on the right side.
3. [tex]\(10n = n - 3\)[/tex]
This equation perfectly matches our algebraic representation. It states that the product of 10 and [tex]\( n \)[/tex] is 3 less than the number [tex]\( n \)[/tex].
4. [tex]\(\frac{10}{n} = n - 3\)[/tex]
This equation states that 10 divided by [tex]\( n \)[/tex] equals [tex]\( n \)[/tex] minus 3, which also does not match our algebraic representation.
Based on our verification, the correct answer is:
[tex]\[ 10n = n - 3 \][/tex]
Therefore, the equation that represents this number sentence is:
[tex]\[ \boxed{10n = n - 3} \][/tex]
