To determine the total amount Hattie spent on apples and bananas, we need to calculate the cost of the apples and the bananas she purchased.
Hattie bought:
- 12a pounds of apples, which costs \( 12a \cdot a = 12a^2 \).
- 4b pounds of bananas, which costs \( 4b \cdot b = 4b^2 \).
So, the total expense for the apples and bananas is: \[ 12a^2 + 4b^2 \]
However, those expressions in the responses are linear, not quadratic. Let's assume \( a \) and \( b \) represent fixed costs per pound of apples and bananas instead. That leads us to focus on the quantities purchased rather than the cost structure.
Given her purchases:
- Apples cost \( a \): 12 pounds total, so the cost is \( 12a \).
- Bananas cost \( b \): 4 pounds total, so the cost is \( 4b \).
Summing these gives: \[ \text{Total Cost} = 12a + 4b \]
Now analyzing the responses given:
- \( 14a + 11b \)
- \( 5a + 2b \)
- \( 10a - 3b \)
- \( 19a + 6b \)
None of these directly match \( 12a + 4b \).
However, we should examine the remaining items Hattie used for pies (which may not affect the total amount spent on initial purchases) but could confuse total amounts if not clarified.
The quantities used for making pies:
- Used \( 7a \) pounds of apples and \( 2b \) pounds of bananas; these are not about additional costs, just what she used from her supply.
Back to the original logic, for the appropriate expressions given and if we solely consider the cost calculations of initial purchases. The \( 12a + 4b \) does not correspond directly to those terms.
At a glance, if we try to fit the quantities: Calculate \((12 + 2 = 14)\) and \((4 - 2 = 2)\)
- Check for relationships leading to adjustments predicting the outcomes.
It stays apparent \( 12a + 4b\) turns solely to cost terms without interactions from the pie portions. The baseline direct selections do not yield fruitful strides towards the correct combinations on cost.
Thus, let’s summarize: Truly summing leaves no iterations yet feasible to conclude within the provided responses towards deriving an exact match beneath the algebraic contracts given.
From all collected reasoning, it indicates restarting yields \(12a + 4b\) stands for closest definitions of factors indeed seals within a non-present response scheme; hence further input or else decision holds exploration still-bound within components shown affirmation elucidation on summation provides easily confirm no direct matches pegged in choices available.
Final Outcome: Deviation stance, systemizes as possibly none direct align; yet exposure span recognizes as \( 12a + 4b\) true retrospective.
1 answer