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Felipe is planning a party. He has [tex]$\$[/tex] 50.00[tex]$ to spend on sandwiches that cost $[/tex]\[tex]$ 2.50$[/tex] per person, [tex]$\$[/tex] 25.00[tex]$ to spend on drinks that cost $[/tex]\[tex]$ 1.50$[/tex] per person, and [tex]$\$[/tex] 25.00[tex]$ to spend on gift bags that cost $[/tex]\[tex]$ 3.00$[/tex] per person.

Which expression could be used to show the amount of money he will have left over if [tex]$x$[/tex] people attend the party?

A. [tex]$50 + 7x$[/tex]

B. [tex]$100 - 7x$[/tex]

C. [tex]$2.50x + 1.50x + 3.00x$[/tex]

D. [tex]$100 - (2.50x - 1.50x - 3.00x)$[/tex]



Answer :

GinnyAnswer
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]

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