To determine how many matching outfits Sheila can buy with her gift card, we first need to set up an inequality based on the total amount on the gift card and the cost of one matching set.
1. Create and Solve an Inequality
Let's denote:
- \( G \) = total amount on the gift card
- \( C \) = cost of one matching 3-piece outfit
Sheila wants to buy \( x \) matching outfits. The total cost of \( x \) matching outfits would be \( 3Cx \) (since each outfit consists of 3 items). The inequality will look like this:
\[ 3Cx \leq G \]
To find the maximum number of outfits, we can solve for \( x \):
\[ x \leq \frac{G}{3C} \]
Example Calculation
Assuming the value of the gift card \( G \) is $100, and the cost of each item \( C \) is $10, the inequality will be:
\[ 3(10)x \leq 100 \]
This simplifies to:
\[ 30x \leq 100 \]
Dividing both sides by 30 gives:
\[ x \leq \frac{100}{30} \approx 3.33 \]
Since \( x \) must be a whole number (you cannot buy a fraction of an outfit), the greatest number of outfits she can buy is:
\[ x = 3 \]
2. How Much Money Is Left on the Gift Card After This Purchase?
If Sheila buys 3 matching outfits, the total cost would be:
\[ \text{Total Cost} = 3 \times 3C = 9C \]
Using our previous example where \( C = 10 \):
\[ 9C = 9 \times 10 = 90 \]
Finally, the amount left on the gift card would be:
\[ \text{Money Left} = G - \text{Total Cost} = 100 - 90 = 10 \]
3. Could There Be Another Combination of Items That Could Have Left Less Money on the Gift Card?
To determine if a different combination could leave less money, Sheila can try adjusting the cost per item if possible and see if she can still maximize the number of outfits purchased. However, adding more expensive items would reduce the number of outfits she can buy due to the fixed budget, which would typically lead to more money remaining on the gift card.
The best approach is for her to consider the price of each item and remain within the constraints of the inequality previously established.
4. What Organized Process Can Sheila Use to Manage the Different Combinations of Items in an Efficient Manner?
Sheila can take several steps to manage her purchases:
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Update Costs and Budget: Maintain a list of the prices of items she is considering for matching outfits.
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Create a Table: Create a simple table or spreadsheet to evaluate different combinations of items and their cumulative costs. For instance:
| Outfit Option | Cost per Item | Total Cost | Outfits Possible | Money Left | |---------------|----------------|------------|------------------|------------| | Option 1 | $10 | $30 | 3 | $10 | | Option 2 | $15 | $45 | 2 | $10 | | Option 3 | $8 | $24 | 4 | $4 |
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Evaluate Options: Regularly analyze these combinations to find the maximum number of outfits while monitoring how much money might remain.
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Calculate Remaining Budget: After establishing which combinations fit the inequality, she should always calculate how much remains after each option to ensure the most efficient use of her budget.
By using this organized process, Sheila can effectively gauge her purchases and make informed decisions based on her preferences and budget constraints.
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