What Expression Represents The Total Amount Lisa Pays For An Aquarium Costing $139, B Gold Barbs, And G Guppies?

When visiting a pet store, the costs can quickly add up, especially with the allure of vibrant fish and the necessary equipment to keep them happy and healthy. In this article, we'll delve into a scenario where Lisa embarks on a pet store trip to purchase an aquarium and some colorful fish. Our main goal is to construct an expression that accurately represents the total amount Lisa spends. We'll break down the components of her purchase – the aquarium, the gold barbs, and the guppies – and formulate an algebraic expression that captures the overall cost. This exercise not only reinforces mathematical concepts but also provides a practical application of algebra in everyday situations. So, let's dive in and explore how we can represent Lisa's pet store expenditure using a mathematical expression.

Understanding the Components of Lisa's Purchase

To begin, let's carefully dissect the information provided. We know that Lisa purchases an aquarium that costs $139. This is a fixed cost – a one-time expense that doesn't depend on any other variables. She also buys b gold barbs and g guppies. Here, b and g represent the number of each type of fish Lisa buys, and these are our variables. To determine the total cost, we need to know the price of each gold barb and each guppy. Without this information, we can only represent the cost of the fish in terms of b and g. Let's assume the cost of each gold barb is $x and the cost of each guppy is $y. Now we have all the necessary components to build our expression.

The fixed cost is the price of the aquarium, which is $139. The variable costs are the costs of the gold barbs and the guppies, which depend on the number of each fish Lisa buys. If each gold barb costs $x, then the total cost of the gold barbs is b * x, or $bx. Similarly, if each guppy costs $y, then the total cost of the guppies is g * y, or $gy. To find the total amount Lisa spends, we need to add the fixed cost (the aquarium) and the variable costs (the fish). This gives us the expression: 139 + bx + gy.

This expression beautifully captures the total cost of Lisa's pet store trip. The $139 represents the aquarium, bx represents the total cost of the gold barbs (where b is the number of gold barbs and x is the cost per gold barb), and gy represents the total cost of the guppies (where g is the number of guppies and y is the cost per guppy). This expression is a versatile tool; by substituting different values for b, g, x, and y, we can calculate the total cost for various scenarios. For instance, if gold barbs cost $2 each and guppies cost $1 each, and Lisa buys 5 gold barbs and 10 guppies, we can plug these values into the expression to find the total amount Lisa spends. This application of algebra provides a practical way to manage personal finances and understand how costs accumulate in real-world situations.

Constructing the Expression for Total Cost

Now, let's put it all together. The total amount Lisa pays is the sum of the cost of the aquarium, the cost of the gold barbs, and the cost of the guppies. We already know the cost of the aquarium is $139. We've also established that the cost of b gold barbs at $x each is $bx, and the cost of g guppies at $y each is $gy. Therefore, the expression that represents the total amount Lisa pays is:

Total Cost = Aquarium Cost + (Number of Gold Barbs * Cost per Gold Barb) + (Number of Guppies * Cost per Guppy)

Total Cost = 139 + bx + gy

This expression is a concise and accurate representation of the total amount Lisa spends at the pet store. It incorporates both the fixed cost of the aquarium and the variable costs associated with the fish. The use of variables allows us to easily calculate the total cost for different quantities of fish and different prices. This expression also highlights the power of algebraic notation in representing real-world scenarios. By using variables and mathematical operations, we can create a model that captures the essence of a situation and allows us to make calculations and predictions. This skill is invaluable not only in mathematics but also in various fields such as finance, economics, and engineering.

Moreover, this expression is not just a mathematical formula; it's a story told in symbols. It tells the story of Lisa's trip to the pet store, her decision to buy an aquarium, and her choice of gold barbs and guppies. Each term in the expression represents a specific aspect of her purchase, and the entire expression represents the total cost of her adventure. This narrative aspect of mathematical expressions can make them more engaging and easier to understand. By connecting mathematical concepts to real-world scenarios, we can make learning more meaningful and memorable. This approach fosters a deeper appreciation for mathematics and its role in our lives.

Refining the Expression with Given Information

In the original problem statement, we are given the cost of the aquarium ($139) and the variables b and g representing the number of gold barbs and guppies, respectively. However, we are not given the cost per gold barb or the cost per guppy. Therefore, we must assume that these costs are unknown and should be represented by variables. Let's continue to use x for the cost per gold barb and y for the cost per guppy. With this understanding, the expression we derived earlier, 139 + bx + gy, remains the most accurate representation of the total cost.

This expression is a powerful tool because it allows us to calculate the total cost for any number of gold barbs and guppies, as long as we know the cost per fish. It also demonstrates the importance of variables in algebra. Variables allow us to represent unknown quantities, which is essential for solving problems in mathematics and other fields. In this case, the variables b, g, x, and y allow us to create a general expression that applies to any scenario involving Lisa's purchase of an aquarium, gold barbs, and guppies. This flexibility is one of the key advantages of using algebraic expressions.

Furthermore, this exercise highlights the importance of careful reading and analysis of problem statements. It's crucial to identify what information is given and what information is missing. In this case, the problem statement provides the cost of the aquarium and the variables representing the number of fish, but it does not provide the cost per fish. This omission necessitates the use of additional variables to represent the unknown costs. This process of identifying missing information and making appropriate assumptions is a critical skill in problem-solving, not only in mathematics but also in real-life situations. By carefully analyzing the problem statement and identifying the key components, we can develop a clear and accurate representation of the situation.

Practical Application of the Expression

Let's consider a practical example. Suppose gold barbs cost $2 each and guppies cost $1.50 each. Lisa decides to buy 5 gold barbs and 8 guppies. Using our expression, we can calculate the total cost:

Total Cost = 139 + (5 * 2) + (8 * 1.50)

Total Cost = 139 + 10 + 12

Total Cost = $161

This calculation demonstrates how easily we can find the total cost once we have the values for the variables. The expression 139 + bx + gy serves as a versatile tool for budgeting and financial planning. Lisa can use this expression to estimate the cost of different combinations of fish and make informed decisions about her purchases. This practical application of algebra highlights its relevance in everyday life. From managing personal finances to making business decisions, algebraic expressions provide a powerful framework for analyzing and solving problems.

This example also underscores the importance of understanding the order of operations in mathematics. We first perform the multiplication operations (5 * 2 and 8 * 1.50) and then the addition operations. Following the correct order of operations ensures that we arrive at the correct answer. This fundamental principle of mathematics is essential for accurate calculations and problem-solving. By mastering the order of operations, we can confidently tackle more complex expressions and equations. This skill is crucial not only in mathematics but also in various scientific and technical fields.

Generalizing the Expression for Other Scenarios

The expression 139 + bx + gy can be generalized to represent similar scenarios involving fixed costs and variable costs. For example, if Lisa were to buy other items at the pet store, such as decorations or food, we could add terms to the expression to represent these additional costs. Let's say Lisa also buys d decorations at $z each. The total cost of the decorations would be $dz, and the expression for the total amount Lisa spends would become:

Total Cost = 139 + bx + gy + dz

This generalized expression illustrates the power of algebraic notation in representing complex situations. By adding terms to the expression, we can account for additional variables and factors. This adaptability is one of the key strengths of algebraic models. They can be tailored to fit a wide range of scenarios, making them a valuable tool for analysis and decision-making. In this case, the generalized expression allows us to calculate the total cost of Lisa's pet store trip, including the aquarium, fish, and decorations.

Moreover, this generalization highlights the importance of abstraction in mathematics. By abstracting the key components of the problem (fixed cost, variable costs), we can create a general expression that applies to a variety of situations. This ability to abstract and generalize is a hallmark of mathematical thinking. It allows us to see patterns and relationships that might not be apparent at first glance. By developing our abstract thinking skills, we can gain a deeper understanding of the world around us and solve problems more effectively. This skill is essential not only in mathematics but also in various other disciplines, such as computer science, engineering, and economics.

Conclusion: The Power of Algebraic Expressions

In conclusion, the expression 139 + bx + gy accurately represents the total amount Lisa pays for the aquarium, gold barbs, and guppies. This exercise demonstrates the power of algebraic expressions in modeling real-world situations. By using variables to represent unknown quantities, we can create a concise and versatile expression that allows us to calculate the total cost for different scenarios. This skill is invaluable not only in mathematics but also in various fields such as finance, economics, and engineering. Understanding how to construct and interpret algebraic expressions is a fundamental skill that empowers us to analyze and solve problems in a variety of contexts.

This exploration also highlights the importance of breaking down complex problems into smaller, more manageable components. By identifying the fixed costs and variable costs, we can systematically build an expression that captures the essence of the situation. This problem-solving strategy is applicable not only in mathematics but also in many other areas of life. By learning to break down complex problems, we can approach challenges with confidence and develop effective solutions. This skill is crucial for success in both academic and professional pursuits.

Furthermore, this exercise underscores the connection between mathematics and the real world. Mathematical concepts are not just abstract ideas; they are tools that we can use to understand and solve problems in our daily lives. By applying mathematical principles to practical situations, we can gain a deeper appreciation for the power and relevance of mathematics. This connection between theory and practice is essential for effective learning. By seeing how mathematical concepts apply to the real world, we can make learning more meaningful and memorable.

repair-input-keyword: What expression represents the total amount Lisa pays for an aquarium costing $139, b gold barbs, and g guppies?

title: Expression for Total Aquarium Cost with Fish Gold Barbs and Guppies