To solve this problem, let's break down the expenses based on what's given.
- Taylor's mom has a budget of $150.
- She knows that the food will cost $5 per person, and there are 12 friends coming to the party.
- We need to determine the expression that represents the total budget using \( m \) as the cost of each guest goody bag.
The total cost for food for the 12 friends is: \[ 5 \text{ (cost per person)} \times 12 \text{ (number of people)} = 60 \text{ dollars} \]
Let \( m \) be the cost of each goody bag. Since there are 12 friends at the party, the total cost for the goody bags will be: \[ 12m \]
Now, we need to combine the costs of the food and the goody bags, which must equal the budget: \[ 12m + 60 = 150 \]
However, we want the expression that represents the amount of money Kevin's mom has to spend on each guest's goody bag. We can rearrange the equation for \( m \): \[ 12m + 60 = 150 \] Subtract 60 from both sides: \[ 12m = 150 - 60 \] \[ 12m = 90 \] Now, divide by 12: \[ m = \frac{90}{12} \] \[ m = 7.5 \]
This leads us back to the interpretation of the answer. We need to see which choice matches the appropriate equation.
Out of the options provided:
A. \( 12m + 5 = 150 \) – Incorrect (it doesn’t relate correctly to the spending) B. \( 5(m + 13) = 150 \) – Incorrect (it miscalculates total cost) C. \( m + 12(5) = 150 \) – Correctly formulates to solve for goody bag costs, changing cost structure) D. \( 12(m + 5) = 150 \) – Incorrect (misinterprets the cost relationship)
Among these, Option C is the closest way of expressing the cost: \( m + 12(5) = 150 \) represents \( m \) as cost of each guest goody bag, adding food costs appropriately.
So, the right expression is C: \( m + 12(5) = 150 \).