Clara is planning a party. She has budgeted $30 to spend on sandwiches that cost $2.50 per

Question

person, $25 to spend on drinks that cost $1.50 per person, and $25 to spend on gift bags that
cost $3 per person. How much money will Clara have left over if x people attend the party,
including herself?

Food: 30 - _
Drinks: 25 - 1.5x
Gifts: _ - 3x

Combine the expression.

(30 - 2.5x) + (25 - 1.5x) + (25 - 3x)
30 + 25 + 25 - 2.5x _ - 3x
80 + x (_)
_

This represents the amount of money of the $80 she originally budgeted that she would have left over.
So if 5 friends, including herself, came to the party, she'd have $_ remaining.

Answer 1

Let's break down the amounts Clara has budgeted and how much she spends for \( x \) people attending the party.

Budgeted Amounts:

• For sandwiches: $30, cost per person is $2.50
• For drinks: $25, cost per person is $1.50
• For gift bags: $25, cost per person is $3

Expenses:

• Amount spent on sandwiches for \( x \) people: \( 2.50x \)
• Amount spent on drinks for \( x \) people: \( 1.50x \)
• Amount spent on gift bags for \( x \) people: \( 3x \)

Total Spending: To find out how much total money is spent, we sum all expenses: \[ \text{Total spent} = 2.50x + 1.50x + 3x = (2.50 + 1.50 + 3)x = 7x \]

Remaining Money: Clara's total budget is \[ 30 + 25 + 25 = 80 \] Therefore, the amount of money remaining after the expenses is \[ 80 - 7x \]

Substituting \( x = 5 \) (for 5 friends, including herself): Now, substituting \( x = 5 \): \[ \text{Remaining money} = 80 - 7(5) = 80 - 35 = 45 \]

So, if 5 friends, including herself, came to the party, Clara would have $45 remaining.