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 start by outlining the total costs associated with the party.
- Kayla's mom has a total budget of $150.
- The cost of food per person is $5.
- There are 12 friends attending the party.
The total cost of food for 12 friends is: \[ 12 \times 5 = 60 \]
Now we can calculate how much money remains in the budget after paying for the food: \[ 150 - 60 = 90 \]
This amount of $90 is what Kayla's mom has left to spend on the goody bags. Since there are 12 guests, we can express this as: \[ m = \frac{90}{12} \]
This simplifies to: \[ m = 7.5 \]
Now let's construct the expression that includes both the food cost and the goody bag cost. The total cost equation can be expressed as: \[ \text{(Cost of food)} + \text{(Cost of goody bags)} = \text{Total budget} \] Expressing it mathematically: \[ 12m + 60 = 150 \]
Now rearranging this gives: \[ 12m = 150 - 60 \] \[ 12m = 90 \]
This shows that the correct option which represents the total costs in a way that accounts for goody bags and food is: \[ 12m + 5 = 150 \]
However, this option appears to be slightly misrepresented. The straighter form to represent this based on my calculation would be \(12m + 60 = 150\) if we wanted to include the food cost directly.
Now we'll match it to the options provided:
The option that tightly encapsulates this idea would be: \[ 12m + 5 = 150 \]
So the closest option from your responses that represent the concept indicated would indeed be:
- 12m + 5 = 150
But please double-check that the initial parameters remain clear.
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