Calculating The Mass Of Lady Fingers And Holland Onions

by ADMIN 56 views

In this mathematical exploration, we delve into a real-world scenario involving the purchase of vegetables. Our primary objective is to determine the mass, in kilograms, of lady fingers (Kacang bendi) bought by Fatimah, given the prices of Holland onions (Bawang Holland) and lady fingers, along with the total amount she spent. This problem requires us to utilize our understanding of algebraic equations and problem-solving techniques to arrive at the solution. Let's embark on this mathematical journey and unravel the mystery of the vegetables!

Understanding the Problem

Before we jump into the calculations, let's carefully analyze the information provided in the problem statement. We are given the following details:

  • The price of Holland onions is RM4.50 per kg.
  • The price of lady fingers is RM6.00 per kg.
  • Fatimah spent a total of RM46.50 on both vegetables.

Our goal is to find the mass of lady fingers purchased by Fatimah. To achieve this, we need to establish a relationship between the quantities involved, which can be effectively represented using algebraic equations. Algebraic equations serve as powerful tools for modeling real-world situations and solving for unknown variables.

Setting up the Equations

Let's introduce variables to represent the unknowns in our problem. Let:

  • x be the mass (in kg) of Holland onions purchased.
  • y be the mass (in kg) of lady fingers purchased.

Based on the given information, we can formulate two equations:

  1. Equation 1 (Total cost): The total cost of Holland onions and lady fingers is RM46.50. We can express this as:

    1. 50x + 6.00y = 46.50

    This equation represents the sum of the cost of Holland onions (price per kg multiplied by mass) and the cost of lady fingers (price per kg multiplied by mass), which equals the total amount spent.

  2. Equation 2 (Total mass): We are not directly given the total mass of vegetables purchased. However, we are asked to find the mass of lady fingers, which implies that there must be a relationship between the masses of the two vegetables. Let's assume, for the sake of demonstration, that the total mass of vegetables purchased is known or can be expressed in terms of x and y. If we had additional information about the total mass or a relationship between the masses, we would formulate Equation 2 accordingly. However, since the question directly asks for the mass of lady fingers without providing information about the total mass, we can solve this problem using only Equation 1 if we can deduce the mass of Holland onions or establish another relationship. Let's proceed by trying to solve using only Equation 1 and make a reasonable assumption or look for a hidden constraint.

    In many real-world problems, there might be hidden constraints or assumptions that are not explicitly stated. It's our job to identify these and use them to our advantage.

Solving for the Mass of Lady Fingers

Without additional information to form a second independent equation, we need to rethink our approach. The problem implies a unique solution for the mass of lady fingers, which suggests there might be a constraint we haven't considered. Let's analyze the context of the problem to see if we can find any implicit constraints.

If we assume that the mass of each vegetable purchased is a non-negative value (which is a reasonable assumption in this context), we can explore possible integer or fractional solutions that satisfy Equation 1. This approach might involve trial and error or making an educated guess based on the coefficients in the equation.

Let's rewrite Equation 1:

  1. 50x + 6.00y = 46.50

To simplify the equation, we can divide both sides by 1.50:

3x + 4y = 31

Now we have a simpler equation to work with. We need to find non-negative values for x and y that satisfy this equation. Integer solutions are more likely in practical scenarios involving buying vegetables, so let's explore that possibility first.

We can rearrange the equation to solve for x:

x = (31 - 4y) / 3

Now we can test different integer values for y (starting from 0) and see if we get an integer value for x:

  • If y = 0, x = 31/3 (not an integer)
  • If y = 1, x = (31 - 4) / 3 = 27/3 = 9 (integer!)
  • If y = 2, x = (31 - 8) / 3 = 23/3 (not an integer)
  • If y = 3, x = (31 - 12) / 3 = 19/3 (not an integer)
  • If y = 4, x = (31 - 16) / 3 = 15/3 = 5 (integer!)
  • If y = 5, x = (31 - 20) / 3 = 11/3 (not an integer)
  • If y = 6, x = (31 - 24) / 3 = 7/3 (not an integer)
  • If y = 7, x = (31 - 28) / 3 = 3/3 = 1 (integer!)
  • If y = 8, x = (31 - 32) / 3 = -1/3 (not non-negative)

We have found three possible integer solutions:

  1. x = 9, y = 1
  2. x = 5, y = 4
  3. x = 1, y = 7

Now we need to determine which solution is the most plausible in the given context. Without further information, it's impossible to definitively choose one solution over the others. However, if we had additional information, such as a constraint on the total mass or a preference for one vegetable over the other, we could narrow down the possibilities.

Let's assume for the sake of providing a single answer, that there might be an implicit understanding in the problem context, perhaps from a previous part of the question or a common-sense scenario. If we were to guess, a more balanced purchase might be more likely than an extreme one. For instance, buying 7 kg of lady fingers and only 1 kg of Holland onions (or vice versa) might be less common than buying a more comparable amount of each. Therefore, the solution x = 5, y = 4 seems like a reasonably balanced option.

Final Answer

Based on our calculations and the assumption of a balanced purchase, the mass of lady fingers purchased by Fatimah is approximately 4 kg. This solution is contingent on the assumption we made, and without additional information, other solutions are also possible.

Therefore, the mass of lady fingers is 4 kg.

Conclusion

In this problem, we successfully applied algebraic equations and problem-solving techniques to determine the mass of lady fingers purchased by Fatimah. We learned the importance of carefully analyzing the problem statement, identifying unknowns, and establishing relationships between variables. We also encountered the challenge of dealing with incomplete information and the need to make reasonable assumptions to arrive at a solution. Mathematical problem-solving often involves a combination of logical reasoning, algebraic manipulation, and critical thinking. This exercise highlights the practical application of mathematics in everyday scenarios and reinforces the value of problem-solving skills.

By working through this problem, we've not only found a numerical answer but also honed our mathematical intuition and critical thinking abilities. The beauty of mathematics lies in its ability to model real-world situations and provide us with tools to understand and solve them. Let's continue to explore the world of mathematics and discover its endless possibilities!