You know that the current exchange rate for US dollars (USD) to Indian rupees (INR) is $1: 45.85$, that the exchange rate for Indian rupees to Bangladeshi taka (BDT) is $1: 1.507$, and that the exchange rate for Bangladeshi taka to Myanma kyat (MMK) at a rate of $1: 0.0928$. Which of the following equations is set up properly to calculate the exchange rate from US dollars to Myanma kyat?
a. $(1 USD) \frac{(1 USD)}{(45.85 DNR)} \frac{(1 DNR)}{(1.507 BDT)} \frac{(1 BDT)}{(0.0928 MMK)}=(x MMK)$
b. $(1 USD) \frac{(45.85 DNR)}{(1 USD)} \cdot \frac{(1.507 BDT)}{(45.85 DNR)} \frac{(0.0928 MMK)}{(1.507 BDT)}=(x MMK)$
c. $(1 USD) \frac{(45.85 DNR)}{(1 USD)} \cdot \frac{(1.507 BDT)}{(1 DVR)} \cdot \frac{(0.0928 MMK)}{(1 BDT)}=(x MMKK)$
d. $(I USD) \frac{(I UED)}{(45.85 DNR)} \cdot \frac{(4585 DNR)}{(1.507 BDT)} \cdot \frac{(1.507 BDT)}{(0.0928 MMK)}=(x MMK)$
Please select the best answer from the choices provided
Answer (2)
The correct equation to calculate the exchange rate from US dollars (USD) to Myanma kyat (MMK) is option b: ( 1 U S D ) × ( 1 U S D ) ( 45.85 I NR ) × ( 1 I NR ) ( 1.507 B D T ) × ( 1 B D T ) ( 0.0928 MM K ) = ( x MM K ) . This option correctly cancels out the units and allows for the calculation of the exchange rate as approximately 6.41 MMK for 1 USD.
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Analyze each equation to ensure the units cancel out correctly, leading from USD to MMK.
Option b is the only equation where units cancel out correctly: ( 1 U S D ) ( 1 U S D ) ( 45.85 I NR ) ⋅ ( 1 I NR ) ( 1.507 B D T ) ⋅ ( 1 B D T ) ( 0.0928 MM K ) = ( x MM K ) .
Calculate the final exchange rate: 45.85 × 1.507 × 0.0928 = 6.41210416 .
The correct equation is option b, which calculates the exchange rate from USD to MMK. The final answer is \boxed{b}
Explanation
Understanding the Problem We are given the exchange rates between USD, INR, BDT, and MMK. Our goal is to find the correct equation to calculate the exchange rate from USD to MMK. We need to analyze each option to see which one correctly converts USD to MMK using the given exchange rates.
Analyzing the Options Let's analyze each option:
Option a: ( 1 U S D ) ( 45.85 I NR ) ( 1 U S D ) ( 1.507 B D T ) ( 1 I NR ) ( 0.0928 MM K ) ( 1 B D T ) = ( x MM K ) .
In this option, the units do not cancel out correctly. We have USD in the numerator twice, and MMK in the denominator. This option is incorrect.
Option b: ( 1 U S D ) ( 1 U S D ) ( 45.85 I NR ) ⋅ ( 1 I NR ) ( 1.507 B D T ) ⋅ ( 1 B D T ) ( 0.0928 MM K ) = ( x MM K ) .
In this option, the units cancel out correctly: U S D ⋅ U S D I NR ⋅ I NR B D T ⋅ B D T MM K = MM K So, this option is likely correct.
Option c: ( 1 U S D ) ( 1 U S D ) ( 45.85 I NR ) ⋅ ( 1 D V R ) ( 1.507 B D T ) ⋅ ( 1 B D T ) ( 0.0928 MM K ) = ( x MM KK ) .
There is a typo in this equation: 'DVR' should be 'INR'. Also, the final unit is 'MMKK' which is incorrect. This option is incorrect.
Option d: ( 1 U S D ) ( 45.85 I NR ) ( 1 U E D ) ⋅ ( 1.507 B D T ) ( 4585 I NR ) ⋅ ( 0.0928 MM K ) ( 1.507 B D T ) = ( x MM K ) .
There is a typo in this equation: 'UED' should be 'USD'. Also, the units do not cancel out correctly. This option is incorrect.
Determining the Correct Equation Based on the analysis, option b is the only one where the units cancel out correctly to give the exchange rate from USD to MMK. Therefore, option b is the correct equation.
Calculating the Exchange Rate The correct equation is: ( 1 U S D ) ( 1 U S D ) ( 45.85 I NR ) ⋅ ( 1 I NR ) ( 1.507 B D T ) ⋅ ( 1 B D T ) ( 0.0928 MM K ) = ( x MM K ) This simplifies to: 45.85 ⋅ 1.507 ⋅ 0.0928 = x x = 6.41210416
Examples
Understanding currency exchange rates is essential for international trade, travel, and investment. For example, if a company in the US wants to import goods from Myanmar, they need to convert US dollars into Myanma Kyats to pay the supplier. Knowing the correct exchange rate helps the company accurately calculate the cost of goods and make informed business decisions. Similarly, tourists traveling between countries need to understand exchange rates to manage their travel budgets effectively. This problem demonstrates how to set up the conversion correctly using a chain of exchange rates.
