Master Word Problems: Solve Linear Equations!

Master Word Problems: Solve Linear Equations!

Table of Contents:

1. Introduction
2. Problem one: Cheyenne's bank account
3. Problem two: Remaining kilograms of potatoes
4. Problem three: Cost of creating back to school kits
5. Problem four: Natasha's marathon training

Article:

Introduction

In this article, we will Delve into several mathematical problems and solve them step by step. Each problem presents a unique Scenario and requires the use of equations to find the desired answers. We will cover topics such as bank accounts, shipments of goods, and training for a marathon. So, let's dive into these interesting problem-solving challenges and sharpen our mathematical skills!

Problem one: Cheyenne's bank account

The first problem revolves around Cheyenne's bank account. Cheyenne has $40 in her bank account, and she adds $5 from her allowance to the account every week. We need to write a linear equation to calculate the balance of her account, given the number of weeks she has added money from her allowance.

To do this, we assign the variable Y to represent the balance in Cheyenne's bank account and the variable X to represent the number of weeks. Based on the given information, we can write the equation as follows:

Equation: Y = 5X + 40

This equation represents how the balance in Cheyenne's bank account changes over time. The coefficient of X, 5, represents the amount she adds every week, and the constant term, 40, represents the initial balance.

Now, let's answer the Second part of the problem, which asks for the amount of money in her account after six weeks. We can calculate this by substituting X with 6 in the equation:

*Y = 5 6 + 40 = 30 + 40 = 70**

Therefore, after six weeks, Cheyenne will have $70 in her bank account.

Pros:

• Clear equation to calculate the balance in the bank account.
• Easy to understand and determine the future balance after a specific number of weeks.

Cons:

• None identified.

Problem two: Remaining kilograms of potatoes

The second problem involves a grocery store receiving a shipment of 900 kilograms of potatoes. On average, they sell 25 kilograms of potatoes every day. We need to write an equation to determine the remaining kilograms of potatoes left after a certain number of days.

Let's assign the variable Y to represent the remaining kilograms of potatoes and the variable X to represent the number of days after receiving the shipment. To write the equation, we consider two factors: the initial shipment of potatoes and the daily sales.

Equation: Y = 900 - (25X)

This equation represents the decreasing amount of potatoes as days pass. The initial quantity of potatoes, 900, is subtracted by the daily sales, which is 25 multiplied by X (the number of days).

To find out how many kilograms of potatoes will be left after 10 days, we substitute X with 10 in the equation:

*Y = 900 - (25 10) = 900 - 250 = 650**

Therefore, after 10 days, there will be 650 kilograms of potatoes remaining.

Pros:

• Clear equation to calculate the remaining kilograms of potatoes.
• Provides a straightforward way to determine the remaining quantity after a specific number of days.

Cons:

• None identified.

Problem three: Cost of creating back to school kits

In this problem, we encounter Kyle assembling back-to-school kits. Each kit contains a Pencil, a notebook, and an eraser. The costs of these items are as follows: pencils cost 25 cents each, notebooks cost $1.50 each, and erasers cost 10 cents each. We need to write an equation to Show the total cost of creating a certain number of kits.

Let's assign the variable Y to represent the total cost and the variable X to represent the number of kits. Considering the cost of each item per kit, we can construct the equation:

*Equation: Y = (0.25 X) + (1.50 X) + (0.10 X)**

This equation calculates the overall cost by multiplying the cost of each item by the number of kits. Here, we combine the terms that involve the variable X, resulting in the Simplified equation above.

To answer the question of how much it will cost Kyle to make five kits, we substitute X with 5 in the equation:

*Y = (0.25 5) + (1.50 5) + (0.10 5) = 1.25 + 7.50 + 0.50 = 9.25**

Therefore, it will cost Kyle $9.25 to make five back-to-school kits.

Pros:

• Provides a clear equation to determine the total cost of creating multiple kits.
• Allows easy calculations by substituting the desired number of kits in the equation.

Cons:

• None identified.

Problem four: Natasha's marathon training

Our final problem revolves around Natasha's training for a marathon. In the given scenario, she has run or walked 25 kilometers so far this month. For the remaining training Sessions, she will run three kilometers and walk one kilometer. We need to write an equation showing the total number of kilometers she has trained.

Let's assign the variable Y to represent the total kilometers trained and the variable X to represent the number of times she trains for the rest of the month. Considering the distance covered in each training session, we can formulate the equation:

Equation: Y = 25 + (4X)

This equation accounts for the kilometers Natasha has already covered (25) and the additional distance covered in future training sessions. Since she runs 3 kilometers and walks 1 kilometer in each session, we multiply 4 (3 + 1) by X to obtain the total kilometer value.

To find out how many kilometers Natasha will have run or walked if she trains six more times this month, we substitute X with 6 in the equation:

*Y = 25 + (4 6) = 25 + 24 = 49**

Therefore, if Natasha trains six more times this month, she will have run or walked a total of 49 kilometers.

Pros:

• Presents a clear equation to determine the total kilometers training.
• Allows for easy calculations by substituting the desired number of training sessions in the equation.

Cons:

• None identified.

Conclusion

In this article, we tackled various mathematical problems that required the formulation of equations. We explored Cheyenne's bank account balance, the remaining kilograms of potatoes, the cost of creating back-to-school kits, and Natasha's marathon training. By analyzing the given information and applying mathematical principles, we successfully solved each problem and obtained the desired results. Remember, practice and understanding equations lead to improved problem-solving skills in various real-life scenarios.

Highlights:

• Mathematical problem-solving involving bank accounts, shipments, and training.
• Creation of equations to determine balances, remaining quantities, and costs.
• Substitution of variables to find specific values.
• Empowering problem-solving skills through mathematical understanding.

FAQ:

Q: What are the main topics covered in this article? A: This article covers topics such as bank accounts, shipments of goods, and training for a marathon.

Q: Are the equations provided in the article accurate? A: Yes, the equations provided are accurate, and they represent the situations presented in each problem.

Q: Can these problem-solving techniques be applied in real-life situations? A: Absolutely! These problem-solving techniques can be applied to various real-life scenarios involving finances, inventory management, and personal goals.

Q: What is the significance of initial conditions in these problems? A: Initial conditions play a crucial role in setting the starting point of a situation. They help establish a reference point from which subsequent changes can be measured or predicted.

Q: How can mathematical problem-solving skills be developed? A: Mathematical problem-solving skills can be developed through practice, understanding fundamental concepts, and applying logical thinking to real-life scenarios.