To determine the correct expression representing the amount of money \( m \) that Kayla's mom has left to spend on each guest's goodie bag, we start by calculating the total cost of the food.
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Cost of food for 12 friends: \[ \text{Cost} = 12 \text{ friends} \times 5 \text{ dollars/person} = 60 \text{ dollars} \]
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Remaining budget after food: \[ \text{Remaining budget} = 150 \text{ dollars} - 60 \text{ dollars} = 90 \text{ dollars} \]
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If there are 12 goodie bags and \( m \) represents the amount spent on each goodie bag: The total cost for the goodie bags for 12 guests is \( 12m \).
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Setting up the equation for the remaining budget: \[ 12m = 90 \]
However, the correct expression mentioned in the options needs to relate the remaining budget to both the food cost and the goodie bags. The correct setup of her planning around the total budget incorporated correctly into the choices we have available indicates that:
In the context of the options: Let's express the total costs using a formula:
- The total costs (goodie bags + food) must equal the total budget: \[ 12m + 60 = 150 \]
This is equivalent to determining the expression for \( 12m \) in relation to the total budget minus the food costs, giving us: \[ 12m = 150 - 60 \] or simply rearranging this to express expenditures for each guest.
After looking at all options again:
- A: \( 12(m + 5) = 150 \) — Incorrect, this assumes m adds to food costs.
- B: \( 5(m + 12) = 150 \) — Incorrect for what we're calculating.
- C: \( m + 12(5) = 150 \) — Incorrect in structure, suggests different interpretation.
- D: \( 12m + 5 = 150 \) — Incorrect total relationship.
None appear to directly set \( 12m = 90 \).
From your breakdown of situation and plans: The expression representing that, if you redo the balance based solely on the remaining money after fixing the food cost could effectively come to rather an added total where \(m\) balances appropriately around what gets left after each person.
If forced: Choosing the option which might relate to food coexisting with \(m\) included amidst the 90 after adjustments would focus around mathematical framing bounding within tight numbers rather than base expense driving:
Conclusion should land around \(C\) but focus shifts on building whole fund on goodie bag that referred on m being backend after overall cost to validate individual grouping inclusive by standard sum, E.g. \(m + 60 = 150\).
However the remaining inclusive balances are ultimately derived as \( 12m = 90 \).
Final Interpretation: The closest, although still heaped upon the food element adjustments does tend to circle back—the choices given seem to err based on standard whole sums fundamentally. Choose \(D\)—but utilize context on total outlay directly rather than interactive splitting towards bagging factor discussions!
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