To determine the correct expression representing the amount of money, \( m \), that Kayla's mom has to spend on each guest's goody bag, we need to consider the costs involved:
- The total budget for the party is $150.
- The cost of food is $5 per person, and there are 12 guests coming.
First, we calculate the total cost for the food:
\[ \text{Cost of food} = 12 \times 5 = 60 \]
Now, we subtract the total food cost from the budget to find out how much money is left for goody bags:
\[ \text{Money left for goody bags} = 150 - 60 = 90 \]
Next, we need to determine how much she can spend on each goody bag if there are 12 goody bags for the 12 guests:
\[ \text{Money per guest for goody bags} = \frac{90}{12} = 7.5 \]
However, to represent this in an equation form, we can write it with \( m \) as the amount spent on each guest's goody bag. Since there are 12 guests, the total spent on goody bags would be \( 12m \). Therefore, we can write the equation as:
\[ 150 = 12m + 60 \]
Rearranging this gives us:
\[ 12m = 150 - 60 \] \[ 12m = 90 \]
Thus, the equation that represents the situation can be simplified directly. However, looking at the options provided, the one that most accurately depicts the situation, where \( 12m \) represents the total spent on goody bags plus the food costs, would be:
\[ 12m + 5 \times 12 = 150 \]
From the choices you listed, the correct expression is:
12(m + 5) = 150
This represents the relationship between the total budget, the cost of each guest's goody bag, and the cost of food.
1 answer