Let's solve this step-by-step to determine which algebraic expression correctly represents the given phrase: "five times the sum of a number and eleven, divided by three times the sum of the number and eight."
1. Identify the variable and the operations:
- Let the variable be [tex]\( x \)[/tex].
- The sum of a number and eleven is [tex]\( x + 11 \)[/tex].
- The sum of the number and eight is [tex]\( x + 8 \)[/tex].
2. Multiply the sum of the number and eleven by five:
[tex]\[
5(x + 11)
\][/tex]
3. Multiply the sum of the number and eight by three:
[tex]\[
3(x + 8)
\][/tex]
4. Construct the fraction, where the numerator is five times the sum of the number and eleven and the denominator is three times the sum of the number and eight:
[tex]\[
\frac{5(x + 11)}{3(x + 8)}
\][/tex]
Thus, the correct algebraic expression that represents the given phrase is:
[tex]\[
\frac{5(x+11)}{3(x+8)}
\][/tex]
This matches the third option:
[tex]\[
\frac{5(x+11)}{3(x+8)}
\][/tex]
