Ken Drinks 3 5 \frac{3}{5} 5 3 ​ Of A Litre Of Milk Every Day. Milk Costs £ 2.20 £2.20 £2.20 For A 2-litre Bottle And £ 1.40 £1.40 £1.40 For A 1-litre Bottle. Ken Buys Enough Milk To Last 7 Days. What Is The Lowest Price Ken Can Pay For His Milk? Show

by ADMIN 252 views

Introduction

In this article, we will delve into the world of mathematics and explore a real-life scenario where Ken needs to purchase milk for a week. We will analyze the given information, identify the constraints, and use mathematical techniques to determine the lowest price Ken can pay for his milk.

The Problem

Ken drinks 35\frac{3}{5} of a litre of milk every day. To calculate the total amount of milk he needs for 7 days, we can multiply the daily consumption by 7.

Total milk needed=35×7=215 litres\text{Total milk needed} = \frac{3}{5} \times 7 = \frac{21}{5} \text{ litres}

Milk costs £2.20£2.20 for a 2-litre bottle and £1.40£1.40 for a 1-litre bottle. We need to find the lowest price Ken can pay for his milk, considering the available bottle sizes and prices.

Analyzing the Options

Let's analyze the two available bottle sizes and prices:

  • 2-litre bottle: £2.20£2.20
  • 1-litre bottle: £1.40£1.40

We need to determine the number of bottles Ken should buy to meet his milk requirements. To do this, we can calculate the number of 1-litre bottles needed to cover the total milk requirement.

Number of 1-litre bottles=Total milk needed1-litre bottle size=2151=215\text{Number of 1-litre bottles} = \frac{\text{Total milk needed}}{\text{1-litre bottle size}} = \frac{\frac{21}{5}}{1} = \frac{21}{5}

Since we cannot buy a fraction of a bottle, we need to round up to the nearest whole number. Therefore, Ken needs to buy at least 215≈4.2\frac{21}{5} \approx 4.2 1-litre bottles.

Calculating the Cost

To calculate the cost of the milk, we can multiply the number of bottles by the price per bottle.

Cost of 1-litre bottles=215×£1.40=£5.88\text{Cost of 1-litre bottles} = \frac{21}{5} \times £1.40 = £5.88

However, we also need to consider the 2-litre bottle option. To determine if buying a 2-litre bottle is more cost-effective, we can calculate the number of 2-litre bottles needed to cover the total milk requirement.

Number of 2-litre bottles=Total milk needed2-litre bottle size=2152=2110\text{Number of 2-litre bottles} = \frac{\text{Total milk needed}}{\text{2-litre bottle size}} = \frac{\frac{21}{5}}{2} = \frac{21}{10}

Since we cannot buy a fraction of a bottle, we need to round up to the nearest whole number. Therefore, Ken needs to buy at least 2110≈2.1\frac{21}{10} \approx 2.1 2-litre bottles.

Comparing the Options

Let's compare the cost of the two options:

  • Cost of 1-litre bottles: £5.88
  • Cost of 2-litre bottles: £2.20 \times 2.1 = £4.62

We can see that buying 2-litre bottles is more cost-effective than buying 1-litre bottles.

Conclusion

In conclusion, the lowest price Ken can pay for his milk is by buying 2-litre bottles. To meet his milk requirements for 7 days, Ken needs to buy at least 2.1 2-litre bottles, which will cost him £4.62.

Discussion

This problem requires a combination of mathematical techniques, including multiplication, division, and rounding. It also involves analyzing the given information, identifying the constraints, and using mathematical techniques to determine the lowest price Ken can pay for his milk.

Mathematical Concepts

This problem involves the following mathematical concepts:

  • Multiplication: to calculate the total amount of milk needed
  • Division: to calculate the number of bottles needed
  • Rounding: to round up to the nearest whole number
  • Comparison: to compare the cost of the two options

Real-World Applications

This problem has real-world applications in various fields, including:

  • Finance: to determine the lowest price for a product or service
  • Business: to optimize inventory management and reduce costs
  • Logistics: to determine the most cost-effective way to transport goods

Future Research Directions

This problem can be extended in various ways, including:

  • Considering different bottle sizes and prices
  • Analyzing the impact of inflation on the cost of milk
  • Developing a mathematical model to optimize milk purchases

Q: What is the main goal of this problem?

A: The main goal of this problem is to determine the lowest price Ken can pay for his milk, considering the available bottle sizes and prices.

Q: What is the total amount of milk Ken needs for 7 days?

A: To calculate the total amount of milk Ken needs for 7 days, we multiply the daily consumption by 7.

Total milk needed=35×7=215 litres\text{Total milk needed} = \frac{3}{5} \times 7 = \frac{21}{5} \text{ litres}

Q: What are the available bottle sizes and prices?

A: The available bottle sizes and prices are:

  • 2-litre bottle: £2.20£2.20
  • 1-litre bottle: £1.40£1.40

Q: How do we determine the number of bottles Ken should buy?

A: To determine the number of bottles Ken should buy, we can calculate the number of 1-litre bottles needed to cover the total milk requirement.

Number of 1-litre bottles=Total milk needed1-litre bottle size=2151=215\text{Number of 1-litre bottles} = \frac{\text{Total milk needed}}{\text{1-litre bottle size}} = \frac{\frac{21}{5}}{1} = \frac{21}{5}

Q: Why can't we buy a fraction of a bottle?

A: We can't buy a fraction of a bottle because it's not a feasible option in real-life scenarios.

Q: How do we calculate the cost of the milk?

A: To calculate the cost of the milk, we can multiply the number of bottles by the price per bottle.

Q: What is the cost of the 1-litre bottles?

A: The cost of the 1-litre bottles is:

Cost of 1-litre bottles=215×£1.40=£5.88\text{Cost of 1-litre bottles} = \frac{21}{5} \times £1.40 = £5.88

Q: What is the cost of the 2-litre bottles?

A: The cost of the 2-litre bottles is:

Cost of 2-litre bottles=£2.20×2.1=£4.62\text{Cost of 2-litre bottles} = £2.20 \times 2.1 = £4.62

Q: Which option is more cost-effective?

A: Buying 2-litre bottles is more cost-effective than buying 1-litre bottles.

Q: What is the lowest price Ken can pay for his milk?

A: The lowest price Ken can pay for his milk is by buying 2-litre bottles, which will cost him £4.62.

Q: What mathematical concepts are involved in this problem?

A: The mathematical concepts involved in this problem are:

  • Multiplication: to calculate the total amount of milk needed
  • Division: to calculate the number of bottles needed
  • Rounding: to round up to the nearest whole number
  • Comparison: to compare the cost of the two options

Q: What are the real-world applications of this problem?

A: The real-world applications of this problem include:

  • Finance: to determine the lowest price for a product or service
  • Business: to optimize inventory management and reduce costs
  • Logistics: to determine the most cost-effective way to transport goods

Q: What are some potential extensions of this problem?

A: Some potential extensions of this problem include:

  • Considering different bottle sizes and prices
  • Analyzing the impact of inflation on the cost of milk
  • Developing a mathematical model to optimize milk purchases