An Amount Of Money Is Divided Among A, B, And C In The Ratio $4:7:9$. B Receives R 500 Less Than C. Calculate The Amount That Is Divided. Additionally, Decrease R 3700 In The Ratio Of $2:5$.

An amount of money is divided among A, B, and C in the ratio $4:7:9$. B receives R 500 less than C. Calculate the amount that is divided. Additionally, decrease R 3700 in the ratio of $2:5$

In this article, we will be discussing a problem involving the division of an amount of money among three individuals, A, B, and C, in a specific ratio. We will also be required to decrease a certain amount of money by a given ratio. This problem requires a good understanding of ratios and proportions, as well as the ability to set up and solve equations.

Let's assume that the amount of money is divided among A, B, and C in the ratio $4:7:9$. This means that the total amount of money can be represented as $4x + 7x + 9x = 20x$, where $x$ is a constant factor.

We are also given that B receives R 500 less than C. This can be represented as $7x - 9x = 500$, which simplifies to $-2x = 500$.

To solve for $x$, we can divide both sides of the equation by $-2$, which gives us $x = -250$.

Now that we have the value of $x$, we can calculate the total amount of money by substituting $x$ into the equation $20x$. This gives us $20(-250) = -5000$.

However, we are not done yet. We are also given that B receives R 500 less than C, which means that the amount of money received by B is $7x - 500 = 7(-250) - 500 = -1750 - 500 = -2250$.

Similarly, the amount of money received by C is $9x = 9(-250) = -2250$.

The amount of money received by A is $4x = 4(-250) = -1000$.

The total amount of money is the sum of the amounts received by A, B, and C, which is $-1000 - 2250 - 2250 = -5750$.

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Now, let's move on to the second part of the problem. We are required to decrease R 3700 in the ratio of $2:5$. This means that the amount of money to be decreased can be represented as $2y + 5y = 7y$, where $y$ is a constant factor.

We are given that the amount of money to be decreased is R 3700, which can be represented as $7y = 3700$.

To solve for $y$, we can divide both sides of the equation by $7$, which gives us $y = 529.29$.

Now that we have the value of $y$, we can calculate the amount of money to be decreased by substituting $y$ into the equation $7y$. This gives us $7(529.29) = 3700$.

However, we are not done yet. We are required to decrease R 3700 in the ratio of $2:5$, which means that the amount of money to be decreased is $2y = 2(529.29) = 1058.58$.

The amount of money to be increased is $5y = 5(529.29) = 2654.45$.

In conclusion, the total amount of money is R 5750, and the amount of money to be decreased is R 1058.58. The amount of money to be increased is R 2654.45.

Q: What is the ratio in which the amount of money is divided among A, B, and C?

A: The amount of money is divided among A, B, and C in the ratio $4:7:9$.

Q: What is the relationship between the amounts received by B and C?

A: B receives R 500 less than C.

Q: How do we calculate the total amount of money?

A: We calculate the total amount of money by substituting the value of $x$ into the equation $20x$. This gives us $20(-250) = -5000$.

Q: What is the amount of money received by each individual?

A: The amount of money received by A is $-1000$, by B is $-2250$, and by C is $-2250$.

Q: What is the total amount of money?

A: The total amount of money is $-5750$.

Q: How do we decrease R 3700 in the ratio of $2:5$?

A: We decrease R 3700 in the ratio of $2:5$ by finding the value of $y$ and substituting it into the equation $7y$. This gives us $7(529.29) = 3700$.

Q: What is the amount of money to be decreased?

A: The amount of money to be decreased is $2y = 2(529.29) = 1058.58$.

Q: What is the amount of money to be increased?

A: The amount of money to be increased is $5y = 5(529.29) = 2654.45$.

Q: What is the final answer?

A: The final answer is R 5750.

• Not understanding the ratio: Make sure to understand the ratio in which the amount of money is divided among A, B, and C.
• Not calculating the total amount of money correctly: Double-check your calculations to ensure that you are getting the correct total amount of money.
• Not decreasing the amount of money correctly: Make sure to follow the correct steps to decrease the amount of money in the ratio of $2:5$.

• Use a calculator: Use a calculator to help you with your calculations, especially when dealing with large numbers.
• Check your work: Double-check your work to ensure that you are getting the correct answers.
• Practice, practice, practice: Practice solving similar problems to help you become more comfortable with the concepts.

In conclusion, the total amount of money is R 5750, and the amount of money to be decreased is R 1058.58. The amount of money to be increased is R 2654.45. By following the correct steps and avoiding common mistakes, you can solve this problem with ease.