To determine whether the gerbils can afford the best brand of all items within their $500 budget, we first need to calculate the total cost for each item using the prices of the best brands.
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Butter:
- Quantity: 25 sticks
- Price of Best Butter: $7.00 per stick
- Total cost for butter: \(25 \text{ sticks} \times 7 \text{ dollars/stick} = 175 \text{ dollars}\)
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Milk:
- Quantity: 18 cartons
- Price of Best Milk: $10.00 per carton
- Total cost for milk: \(18 \text{ cartons} \times 10 \text{ dollars/carton} = 180 \text{ dollars}\)
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Paper Towels:
- Quantity: 27 rolls
- Price of Best Paper Towels: $7.00 per roll
- Total cost for paper towels: \(27 \text{ rolls} \times 7 \text{ dollars/roll} = 189 \text{ dollars}\)
Now we add up all the costs:
\[ \text{Total Cost} = \text{Cost of Butter} + \text{Cost of Milk} + \text{Cost of Paper Towels} \] \[ \text{Total Cost} = 175 + 180 + 189 = 544 \text{ dollars} \]
Since the total cost of $544 exceeds their budget of $500, they cannot afford the best brand of all items.
Next, we need to check which items they can spend more on while still staying within the $500 budget. We will explore other combinations to minimize the cost or allow for more expensive brands on some items.
Remaining Budget Analysis
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If they choose the Best Butter:
- Total Cost for Butter: $175
- Remaining budget after Butter: \[ 500 - 175 = 325 \text{ dollars} \]
- Maximum they can spend on Milk and Paper Towels combined while staying within the remaining budget (total cost from best brands): \[ 180 + 189 = 369 \text{ dollars} \quad (\text{Exceeds the budget}) \]
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Total Cost if they choose Good Butter:
- Total Cost for Butter: \(25 \times 2 = 50\) → Good Butter: 50 dollars
- Remaining budget after Good Butter: \[ 500 - 50 = 450 \]
- Maximum they can spend on Milk and Paper Towels combined:
- Total Cost of remaining best brands of Milk and Paper Towels (best prices): \[ 180 + 189 = 369 \text{ dollars} \quad (\text{Under budget}) \]
Now let's check alternate combos with more than Good for either Milk or Paper Towels:
- Good Butter + Great Milk + Best Paper Towels:
- Good Butter (25 at $2): $50
- Great Milk (18 at $6): \(18 \times 6 = 108\)
- Best Paper Towels (27 at $7): \(27 \times 7 = 189\)
- Total Cost: \[ 50 + 108 + 189 = 347 \text{ dollars} \quad (\text{Under budget}) \]
They are able to spend more on combinations and still meet budget, if they utilize combinations of good, great, and best products as shown above.
Conclusion
- The best choice within the $500 might involve multiple items at varying quality:
- Good Butter: $50
- Great Milk: $108
- Best Paper Towels: $189
Ensuring they remain under budget to $(500 - 347 = 153)$. So playing with quality between brands can provide flexibility on what they could purchase while making maximum use of allocated funds.
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