Simplifying and Solving for x

Oct 13, 2025 by magicalceylontours.com 35 views

Introduction

In this article, we will explore a problem involving currency exchange rates. We are given the exchange rates between the US dollar (USD), the Indian rupee (INR), and the Sri Lankan rupee (LKR). We will use these exchange rates to find the value of the Vietnamese dong (VND) and the Singapore dollar (SGD) in terms of the US dollar.

Given Exchange Rates

The exchange rate between the US dollar and the Indian rupee is given by: $${ RV = x + 6 }$$
The exchange rate between the US dollar and the Sri Lankan rupee is given by: $${ US = 5x - 9 }$$
The exchange rate between the Indian rupee and the Sri Lankan rupee is given by: $${ RS = 11 }$$

Setting Up the Equation

To find the value of the Vietnamese dong and the Singapore dollar in terms of the US dollar, we need to set up an equation that relates the exchange rates between the different currencies. We can do this by using the given exchange rates and the fact that the exchange rate between the Indian rupee and the Sri Lankan rupee is equal to 11.

Let's set up the equation:

{ x + 6 + x + 6 = 5x - 9 }

This equation represents the fact that the exchange rate between the US dollar and the Indian rupee is equal to the exchange rate between the US dollar and the Sri Lankan rupee, multiplied by the exchange rate between the Indian rupee and the Sri Lankan rupee.

Simplifying and Solving for x

To simplify the equation, we can combine like terms:

{ 2x + 12 = 5x - 9 }

Next, we can subtract 2x from both sides of the equation to get:

{ 12 = 3x - 9 }

Then, we can add 9 to both sides of the equation to get:

{ 21 = 3x }

Finally, we can divide both sides of the equation by 3 to solve for x:

{ x = 7 }

Finding VT and ST

Now that we have found the value of x, we can use it to find the value of the Vietnamese dong and the Singapore dollar in terms of the US dollar.

The exchange rate between the US dollar and the Vietnamese dong is given by:

{ VT = 2x + 6 }

Substituting the value of x, we get:

{ VT = 2(7) + 6 }

{ VT = 14 + 6 }

{ VT = 20 }

The exchange rate between the US dollar and the Singapore dollar is given by:

{ ST = 5x - 9 }

Substituting the value of x, we get:

{ ST = 5(7) - 9 }

{ ST = 35 - 9 }

{ ST = 26 }

Conclusion

In this article, we used the given exchange rates between the US dollar, the Indian rupee, and the Sri Lankan rupee to find the value of the Vietnamese dong and the Singapore dollar in terms of the US dollar. We set up an equation that related the exchange rates between the different currencies, simplified and solved for x, and then used the value of x to find the value of VT and ST.

Final Answer

The final answer is:

${ VT = 20 }$
${ ST = 26 }$$<br/>$

Q: What is the significance of the exchange rates given in the problem?

A: The exchange rates given in the problem represent the value of one currency in terms of another. For example, the exchange rate RV = x + 6 means that 1 US dollar is equal to x + 6 Indian rupees.

Q: How did you simplify the equation 2x + 12 = 5x - 9?

A: To simplify the equation, we combined like terms. We added 12 to both sides of the equation to get 2x = 5x - 21, and then subtracted 5x from both sides to get -3x = -21. Finally, we divided both sides by -3 to get x = 7.

Q: What is the relationship between the exchange rates VT and ST?

A: The exchange rates VT and ST are related to the exchange rates RV and US. VT is the exchange rate between the US dollar and the Vietnamese dong, while ST is the exchange rate between the US dollar and the Singapore dollar. We used the value of x to find the values of VT and ST.

Q: How did you find the value of VT?

A: We found the value of VT by substituting the value of x into the equation VT = 2x + 6. This gave us VT = 2(7) + 6 = 14 + 6 = 20.

Q: How did you find the value of ST?

A: We found the value of ST by substituting the value of x into the equation ST = 5x - 9. This gave us ST = 5(7) - 9 = 35 - 9 = 26.

Q: What is the significance of the values of VT and ST?

A: The values of VT and ST represent the value of the Vietnamese dong and the Singapore dollar in terms of the US dollar. For example, the value VT = 20 means that 1 US dollar is equal to 20 Vietnamese dong.

Q: Can you explain the concept of exchange rates in more detail?

A: Exchange rates are the prices of one currency in terms of another. They are used to convert the value of one currency into another. For example, if the exchange rate between the US dollar and the Indian rupee is 1 USD = 70 INR, then 1 US dollar is equal to 70 Indian rupees.

Q: How do exchange rates affect international trade?

A: Exchange rates can have a significant impact on international trade. A strong exchange rate can make a country's exports more competitive in the global market, while a weak exchange rate can make imports more expensive. This can affect the balance of trade and the overall economy of a country.

Q: Can you provide more examples of how to use exchange rates to solve problems?

A: Yes, here are a few more examples:

If the exchange rate between the US dollar and the Japanese yen is 1 USD = 110 JPY, and the exchange rate between the Japanese yen and the British pound is 1 JPY = 0.01 GBP, what is the exchange rate between the US dollar and the British pound?
If the exchange rate between the US dollar and the euro is 1 USD = 0.85 EUR, and the exchange rate between the euro and the Swiss franc is 1 EUR = 1.20 CHF, what is the exchange rate between the US dollar and the Swiss franc?
If the exchange rate between the US dollar and the Chinese yuan is 1 USD = 6.50 CNY, and the exchange rate between the Chinese yuan and the Australian dollar is 1 CNY = 0.15 AUD, what is the exchange rate between the US dollar and the Australian dollar?

These are just a few examples of how to use exchange rates to solve problems. The key is to understand the relationships between the different currencies and to use the given exchange rates to find the values of the other currencies.