Sianna Bought 3 Pens, 4 Notebooks, And A Calculator. The Calculator Cost $ 25 \$25 $25 . If X X X Represents The Cost Of Each Pen And Y Y Y Represents The Cost Of Each Notebook, Which Expression Represents The Amount Of Change Sianna

Introduction

In this article, we will explore the concept of cost and change in a real-world scenario. Sianna, a student, bought 3 pens, 4 notebooks, and a calculator. The calculator cost $\$25$. We will use algebraic expressions to represent the cost of each pen and notebook, and then calculate the amount of change Sianna received after making the purchase.

Representing the Cost of Items

Let's assume that the cost of each pen is represented by the variable $x$ and the cost of each notebook is represented by the variable $y$. We can then express the total cost of the items as follows:

• The cost of 3 pens is $3x$.
• The cost of 4 notebooks is $4y$.
• The cost of the calculator is $\$25$.

Calculating the Total Cost

The total cost of the items is the sum of the cost of the pens, notebooks, and calculator. We can express this as:

Total Cost = $3x + 4y + 25$

Calculating the Amount of Change

To calculate the amount of change Sianna received, we need to subtract the total cost from the amount she paid. Let's assume that Sianna paid $\$100$. We can express the amount of change as:

Amount of Change = $100 - (3x + 4y + 25)$

Simplifying the Expression

We can simplify the expression for the amount of change by combining like terms:

Amount of Change = $100 - 3x - 4y - 25$ Amount of Change = $75 - 3x - 4y$

Conclusion

In this article, we used algebraic expressions to represent the cost of each pen and notebook, and then calculated the amount of change Sianna received after making the purchase. We found that the expression for the amount of change is $75 - 3x - 4y$. This expression represents the amount of change Sianna received in terms of the cost of each pen and notebook.

Real-World Applications

This concept of cost and change is essential in real-world scenarios, such as shopping, banking, and finance. Understanding how to calculate the amount of change received after making a purchase is crucial in making informed decisions and managing finances effectively.

Example Problems

1. If the cost of each pen is $\$5$and the cost of each notebook is $\$10$, what is the amount of change Sianna received?
2. If the cost of each pen is $\$3$and the cost of each notebook is $\$8$, what is the amount of change Sianna received?

Solution to Example Problems

1. Substituting the values of $x$ and $y$ into the expression for the amount of change, we get:

Amount of Change = $75 - 3(5) - 4(10)$ Amount of Change = $75 - 15 - 40$ Amount of Change = $20$

Therefore, the amount of change Sianna received is $\$20$.

2. Substituting the values of $x$ and $y$ into the expression for the amount of change, we get:

Amount of Change = $75 - 3(3) - 4(8)$ Amount of Change = $75 - 9 - 32$ Amount of Change = $34$

Therefore, the amount of change Sianna received is $\$34$.

Conclusion

Q: What is the cost of each pen and notebook in the scenario?

A: The cost of each pen is represented by the variable $x$ and the cost of each notebook is represented by the variable $y$. We do not have specific values for $x$ and $y$ in the scenario.

Q: How do I calculate the total cost of the items?

A: The total cost of the items is the sum of the cost of the pens, notebooks, and calculator. We can express this as:

Total Cost = $3x + 4y + 25$

Q: How do I calculate the amount of change Sianna received?

A: To calculate the amount of change Sianna received, we need to subtract the total cost from the amount she paid. Let's assume that Sianna paid $\$100$. We can express the amount of change as:

Amount of Change = $100 - (3x + 4y + 25)$

Q: Can I simplify the expression for the amount of change?

A: Yes, we can simplify the expression for the amount of change by combining like terms:

Amount of Change = $100 - 3x - 4y - 25$ Amount of Change = $75 - 3x - 4y$

Q: What is the amount of change Sianna received if the cost of each pen is $\$5$and the cost of each notebook is $\$10$?

A: Substituting the values of $x$ and $y$ into the expression for the amount of change, we get:

Amount of Change = $75 - 3(5) - 4(10)$ Amount of Change = $75 - 15 - 40$ Amount of Change = $20$

Therefore, the amount of change Sianna received is $\$20$.

Q: What is the amount of change Sianna received if the cost of each pen is $\$3$and the cost of each notebook is $\$8$?

A: Substituting the values of $x$ and $y$ into the expression for the amount of change, we get:

Amount of Change = $75 - 3(3) - 4(8)$ Amount of Change = $75 - 9 - 32$ Amount of Change = $34$

Therefore, the amount of change Sianna received is $\$34$.

Q: Can I use this concept to calculate the amount of change in other scenarios?

A: Yes, this concept can be applied to other scenarios where you need to calculate the amount of change received after making a purchase. Simply substitute the values of the variables into the expression for the amount of change and solve for the result.

Q: What are some real-world applications of this concept?

A: This concept is essential in real-world scenarios, such as shopping, banking, and finance. Understanding how to calculate the amount of change received after making a purchase is crucial in making informed decisions and managing finances effectively.

Q: Can I use algebraic expressions to represent the cost of other items?

A: Yes, you can use algebraic expressions to represent the cost of other items. For example, if you want to represent the cost of a shirt, you can use a variable such as $z$ to represent the cost of the shirt. Then, you can use the expression $z$ to represent the cost of the shirt in your calculations.

Q: How do I know which variable to use to represent the cost of an item?

A: You can choose any variable to represent the cost of an item, as long as you are consistent in your use of the variable. For example, if you choose to use $x$ to represent the cost of a pen, you should use $x$ consistently throughout your calculations to represent the cost of the pen.