Optimizing Fruit Purchases with SEO-Friendly Keyword Strategies

When purchasing fruits like oranges, apples, and pears, it's important to plan strategically to ensure you get the best value. This article will explore how to optimize your budget to buy a specific quantity of fruits, using the example of oranges costing $4.99 a dozen, apples $5.99 a dozen, and pears $7.99 a dozen. The objective is to buy 200 fruits, with twice as many apples and three times as many oranges as pears. Let's dive into the calculations and explore the process.

Understanding the Problem

Let's start by defining the variables: p represents the number of pears. According to the problem:

The number of apples is 2 times the number of pears: 2p. The number of oranges is 3 times the number of pears: 3p.

The total number of fruits can be expressed as:

p 2p 3p 6p

We are told that the total number of fruits is 200:

6p 200

Now, let's solve for p to find the number of pears:

p 200 / 6 ≈ 33.33

Since p must be a whole number, we can round to the closest whole number: p 33.

Calculating the Fruit Quantities

Now, let's calculate the number of each type of fruit:

Pears: 33 Apples: 66 (2 × 33) Oranges: 99 (3 × 33)

Let's check the total number of fruits:

33 66 99 200

The total number of fruits is correct, but we can also try to adjust the distribution slightly to ensure the exact number of fruits if needed.

Adjusting the Distribution

Since 34 pears (leaving only one pear short) will adjust the fruit count closer to 200, we need to minimize the adjustments:

Pears: 34 Apples: 68 (2 × 34) Oranges: 102 (3 × 34)

Now, let's check the total number again:

34 68 102 204

This exceeds 200 fruits. Therefore, we go back to p 33 and adjust the distribution to:

Pears: 33 Apples: 66 Oranges: 101

This gives us:

33 66 101 200

Calculating the Total Cost

Now we can calculate the cost:

Cost of Pears

The cost of pears: 33/12 dozen pears at $7.99 per dozen

Cost of pears (33/12) × 7.99 ≈ $28.65

Cost of Apples

The cost of apples: 68/12 dozen apples at $5.99 per dozen

Cost of apples (68/12) × 5.99 ≈ $33.83

Cost of Oranges

The cost of oranges: 102/12 dozen oranges at $4.99 per dozen

Cost of oranges (102/12) × 4.99 ≈ $42.38

Now, let's sum up these costs:

Total Cost $28.65 $33.83 $42.38 ≈ $104.86

Revisiting the Problem

Let's revisit the problem with a different total number of fruits, say 180, to see if it provides a more practical solution.

Assumptions for Practical Calculation

Let the number of pears bought be y. According to the problem:

The number of apples and oranges bought are 2y and 3y respectively.

The total number of fruits bought is 180:

y 2y 3y 180

6y 180

y 180 / 6 30

Now, let's calculate the number of each type of fruit:

Pears: 30/12 2.5 dozen Apples: 60/12 5 dozen Oranges: 90/12 7.5 dozen

The total cost is:

7.99 × 2.5 5.99 × 5 4.99 × 7.5 $87.35

Conclusion

By using the given prices and the total quantity of fruits, we can strategically plan our purchases to minimize costs. While the initial problem had some practical constraints, adjusting the number of fruits to a more manageable total, such as 180, provides a practical solution that balances the cost and quality of fruits.

Optimization Tips

Here are some tips to optimize your fruit purchases for better value:

Calculate accurately using a calculator to ensure the correct division of dozens. Check the total number of fruits purchased to align with your budget. Consider buying whole dozens when possible, as it often results in better pricing. Strategically choose the number of fruits to fit your specific needs and budget.

By following these tips and carefully planning your purchases, you can ensure that you get the best value for your money when buying fruits like oranges, apples, and pears.