To find the correct expression representing the amount of money \( m \) that Kayla’s mom has to spend on each guest’s goody bag, we start by calculating the total cost of the food and then subtract this from the budget to determine what remains for the goody bags.
- Budget: $150
- Cost of food per person: $5
- Number of friends: 12
First, we calculate the total cost of the food:
\[ \text{Total cost of food} = \text{Cost per person} \times \text{Number of people} = 5 \times 12 = 60 \]
Next, we find the remaining budget after covering the cost of food:
\[ \text{Remaining budget} = \text{Total budget} - \text{Total cost of food} = 150 - 60 = 90 \]
Now, the remaining $90 needs to be divided among the 12 guests to buy goody bags. Thus, the amount of money per goody bag (amount for each guest, \( m \)) is:
\[ m = \frac{90}{12} \]
To find an expression, we can represent this remaining amount mathematically. The correct expression should include the total budget, the expense on food, and equate that to the goody bags.
From the options provided, we analyze:
- Option 1: \( 12(m + 5) = 150 \)
- Option 2: \( 12m + 5 = 150 \)
- Option 3: \( m + 12(5) = 150 \)
- Option 4: \( 5(m + 12) = 150 \)
The correct expression that captures that the total cost (goody bags + cost of food) equals the budget is:
Option 3: \( m + 12(5) = 150 \)
This means you are adding the total cost of the goody bags (which is \(12m\)) to the total cost of the food (which is \(12 \times 5\)) to equal the total budget.
So, the expression calculates out as follows:
\[ 12m + 60 = 150 \]
This shows how much \( m \) is available after the food cost is accounted for. Thus, Option 3 is the correct answer.