Question
Kayla’s mom is planning her birthday party. She has a budget of $150. She knows that the food will cost $5 per person. Twelve friends are coming to the party. Which expression represents the amount of money, m, Kayla’s mom has to spend on each guest’s goody bag?(1 point)
Responses
5(m+12)=150
5 Left Parenthesis m plus 12 Right Parenthesis equals 150
12(m+5)=150
12 Left Parenthesis m plus 5 Right Parenthesis equals 150
m+12(5)=150
m plus 12 Left Parenthesis 5 Right Parenthesis equals 150
12m+5=150
Responses
5(m+12)=150
5 Left Parenthesis m plus 12 Right Parenthesis equals 150
12(m+5)=150
12 Left Parenthesis m plus 5 Right Parenthesis equals 150
m+12(5)=150
m plus 12 Left Parenthesis 5 Right Parenthesis equals 150
12m+5=150
Answers
GPT-4o mini
To represent the amount of money, \( m \), that Kayla's mom has to spend on each guest's goody bag, we need to account for the costs of both the food and the goody bags.
1. The cost of food for 12 friends at $5 each is \( 12 \times 5 = 60 \).
2. The total budget is $150.
3. Therefore, the amount left for goody bags after paying for food is \( 150 - 60 = 90 \).
Now, since there are 12 guests, the cost of the goody bags for each guest can be described as total cost for goody bags divided by the number of guests, which is \( \frac{90}{12} \).
To create an expression that represents this situation correctly, we can relate the money spent on goody bags (the expression for the total cost of the goody bags \( 12m \)):
Total budget = Cost of food + Cost of goody bags
This translates into the equation:
\[ 150 = 60 + 12m \]
Rearranging this gives us:
\[ 12m = 150 - 60 \]
\[ 12m = 90 \]
From the options given, \( 12m + 5 = 150 \) does not accurately represent the situation because it incorrectly combines unknowns and fixed amounts. The revised equation matches equally distributed amounts left after food expenses.
However, the best representation of the costs is not directly in the given answers. Since none of them correctly represent \( 12m = 90 \), if we consider the correct form should opt for expressing the goody bag cost under the budget constraint of food.
In terms of expression given:
The best choice closely related to the idea initiated would be:
**None directly match but simply**:
Option \(12(m+5)=150 \) can be reinterpreted but is logically misleading against derived budget calculation since each guest doesn't add solely the goody.
Thus the distinct answer, logically \( \mathbf{m + 12(5) = 150} \) directly embodies the additional cost effectively since \(m*12\) encapsulates.
So the logically fitting, yet by provided options if necessary to opt we referred back value-wise. Considering mismatches with totality would configure \( m+12(5)=150\).
Final insightful take:
**Goody bags beyond** logical correctness should be relatable distinctly _in terms of budget distribution_ and clarify would simply decompose underlying resultant elements on available data against total effectively accounted would likely shred decisive choices accurately amidst them in given choices.
1. The cost of food for 12 friends at $5 each is \( 12 \times 5 = 60 \).
2. The total budget is $150.
3. Therefore, the amount left for goody bags after paying for food is \( 150 - 60 = 90 \).
Now, since there are 12 guests, the cost of the goody bags for each guest can be described as total cost for goody bags divided by the number of guests, which is \( \frac{90}{12} \).
To create an expression that represents this situation correctly, we can relate the money spent on goody bags (the expression for the total cost of the goody bags \( 12m \)):
Total budget = Cost of food + Cost of goody bags
This translates into the equation:
\[ 150 = 60 + 12m \]
Rearranging this gives us:
\[ 12m = 150 - 60 \]
\[ 12m = 90 \]
From the options given, \( 12m + 5 = 150 \) does not accurately represent the situation because it incorrectly combines unknowns and fixed amounts. The revised equation matches equally distributed amounts left after food expenses.
However, the best representation of the costs is not directly in the given answers. Since none of them correctly represent \( 12m = 90 \), if we consider the correct form should opt for expressing the goody bag cost under the budget constraint of food.
In terms of expression given:
The best choice closely related to the idea initiated would be:
**None directly match but simply**:
Option \(12(m+5)=150 \) can be reinterpreted but is logically misleading against derived budget calculation since each guest doesn't add solely the goody.
Thus the distinct answer, logically \( \mathbf{m + 12(5) = 150} \) directly embodies the additional cost effectively since \(m*12\) encapsulates.
So the logically fitting, yet by provided options if necessary to opt we referred back value-wise. Considering mismatches with totality would configure \( m+12(5)=150\).
Final insightful take:
**Goody bags beyond** logical correctness should be relatable distinctly _in terms of budget distribution_ and clarify would simply decompose underlying resultant elements on available data against total effectively accounted would likely shred decisive choices accurately amidst them in given choices.