To determine which variable expression represents the phrase "the sum of a number and 10," let's carefully translate the phrase into a mathematical expression step-by-step.
1. Identify the unknown number: When the phrase mentions "a number," we typically use a variable to represent this unknown number. A common choice for a variable is [tex]\( n \)[/tex].
2. Understand the phrase "the sum of ... and ...": In mathematics, the word "sum" indicates addition. Therefore, "the sum of a number and 10" means we need to add the number (represented by [tex]\( n \)[/tex]) to 10.
3. Construct the expression: Combining these pieces, if we want the sum of the number [tex]\( n \)[/tex] and 10, we write it as [tex]\( n + 10 \)[/tex].
Thus, the correct variable expression representing the phrase "the sum of a number and 10" is:
[tex]\[ n + 10 \][/tex]
Now, let's match this with the given options:
- [tex]\( n - 10 \)[/tex]: This represents the difference of the number and 10, not the sum.
- [tex]\( n \div 10 \)[/tex]: This represents the number divided by 10.
- [tex]\( n + 10 \)[/tex]: This correctly represents the sum of the number and 10.
- [tex]\( 10n \)[/tex]: This represents the product of the number and 10.
Therefore, the correct answer is:
[tex]\[ n + 10 \][/tex]
