Let’s solve the problem step by step to find a suitable expression representing the amount of money Felipe will have left over if [tex]\( x \)[/tex] people attend the party.
1. Allocating the Total Money:
Felipe has:
- [tex]$\$[/tex] 50[tex]$ for sandwiches
- $[/tex]\[tex]$ 25$[/tex] for drinks
- [tex]$\$[/tex] 25[tex]$ for gift bags
Total money allocated is:
\[
50 + 25 + 25 = 100 \text{ dollars}
\]
2. Calculating the Cost Per Person:
- The cost per person for sandwiches is $[/tex]\[tex]$2.50$[/tex]
- The cost per person for drinks is [tex]$\$[/tex]1.50[tex]$
- The cost per person for gift bags is $[/tex]\[tex]$3.00$[/tex]
Total cost per person is:
[tex]\[
2.50 + 1.50 + 3.00 = 7 \text{ dollars}
\][/tex]
3. Expression for Total Spending Based on the Number of People ([tex]\( x \)[/tex]):
The total cost for [tex]\( x \)[/tex] people is given by:
[tex]\[
7x \text{ dollars}
\][/tex]
4. Money Left Over:
The amount of money left over after hosting [tex]\( x \)[/tex] people can be determined by subtracting the total cost for [tex]\( x \)[/tex] people from the total allocated money:
[tex]\[
\text{Money Left} = \text{Total Money Allocated} - \text{Total Cost for \( x \) People}
\][/tex]
We already established:
[tex]\[
\text{Total Money Allocated} = 100 \text{ dollars}
\][/tex]
[tex]\[
\text{Total Cost for \( x \) People} = 7x \text{ dollars}
\][/tex]
So the expression for the money left over is:
[tex]\[
\text{Money Left} = 100 - 7x
\][/tex]
From the given options, the correct expression that shows the amount of money Felipe will have left over if [tex]\( x \)[/tex] people attend the party is:
[tex]\[
100 - 7x
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{100 - 7 x}
\][/tex]
