Answer :
Certainly! Let's break down the problem step by step.
The videography team won a monetary prize of [tex]$1350. This amount needs to be distributed equally among \( x \) people on the team. To determine how much each person would receive, we need to divide the total prize amount by the number of team members. The total prize is $[/tex]1350, and the number of people on the team is [tex]\( x \)[/tex]. Therefore, the expression representing how much each person would get if there are [tex]\( x \)[/tex] people on the team would be:
[tex]\[ \frac{1350}{x} \][/tex]
Now, let's evaluate the given options to see which one matches our expression:
- (A) [tex]\(\frac{1350}{x}\)[/tex]: This matches our expression exactly, as it correctly divides the total amount by the number of team members.
- (B) [tex]\(1350 + x\)[/tex]: This represents the sum of the total prize and the number of people, which is incorrect.
- (C) [tex]\(\frac{1350}{5}\)[/tex]: This would only be correct if there are specifically 5 people on the team, and we are given that there are [tex]\( x \)[/tex] people, not necessarily 5.
- (D) [tex]\(1350 - x\)[/tex]: This would subtract the number of team members from the total prize, which is also incorrect.
Therefore, the correct answer is:
[tex]\[ \text{(A) } \frac{1350}{x} \][/tex]
The videography team won a monetary prize of [tex]$1350. This amount needs to be distributed equally among \( x \) people on the team. To determine how much each person would receive, we need to divide the total prize amount by the number of team members. The total prize is $[/tex]1350, and the number of people on the team is [tex]\( x \)[/tex]. Therefore, the expression representing how much each person would get if there are [tex]\( x \)[/tex] people on the team would be:
[tex]\[ \frac{1350}{x} \][/tex]
Now, let's evaluate the given options to see which one matches our expression:
- (A) [tex]\(\frac{1350}{x}\)[/tex]: This matches our expression exactly, as it correctly divides the total amount by the number of team members.
- (B) [tex]\(1350 + x\)[/tex]: This represents the sum of the total prize and the number of people, which is incorrect.
- (C) [tex]\(\frac{1350}{5}\)[/tex]: This would only be correct if there are specifically 5 people on the team, and we are given that there are [tex]\( x \)[/tex] people, not necessarily 5.
- (D) [tex]\(1350 - x\)[/tex]: This would subtract the number of team members from the total prize, which is also incorrect.
Therefore, the correct answer is:
[tex]\[ \text{(A) } \frac{1350}{x} \][/tex]
