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. $(1 \text{ USD }) \frac{(1 \text{ USD })}{(45.85 \text{ INR })} \cdot \frac{(1 \text{ INR })}{(1.507 \text{ BDT })} \frac{(1 \text{ BDT })}{(0.0928 \text{ MMK})}=(x \text{ MMK})$
b. $(1 \text{ USD }) \cdot \frac{(45.85 \text{ INR })}{(1 \text{ USD })} \cdot \frac{(1.507 \text{ BDT })}{(45.85 \text{ INR })} \cdot \frac{(0.0928 \text{ MMK })}{(1.507 \text{ BDT})}=( x \text{ MMK })$
c. $(1 \text{ USD}) \cdot \frac{(45.85 \text{ INR })}{(1 \text{ USD})} \cdot \frac{(1.507 \text{ BDT })}{(1 \text{ INR})} \cdot \frac{(0.0928 \text{ MMK })}{(1 \text{ BDT})}=(x \text{ MMK})$
d. $(1 \text{ USD }) \cdot \frac{(1 \text{ USD })}{(45.85 \text{ INR })} \cdot \frac{(45.85 \text{ INR })}{(1.507 \text{ BDT })} \cdot \frac{(1.507 \text{ BDT })}{(0.0928 \text{ MMK})}=(x \text{ MMK})$
Answer (2)
The correct equation to convert US dollars to Myanma kyat, based on the provided exchange rates, is option c: ( 1 USD ) ⋅ ( 1 USD ) ( 45.85 INR ) ⋅ ( 1 INR ) ( 1.507 BDT ) ⋅ ( 1 BDT ) ( 0.0928 MMK ) = ( x MMK ) . This properly reflects the sequence of conversions needed between the currencies.
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The problem requires converting USD to MMK using given exchange rates.
Option b correctly sets up the conversion: ( 1 USD ) ⋅ ( 1 USD ) ( 45.85 INR ) ⋅ ( 1 INR ) ( 1.507 BDT ) ⋅ ( 1 BDT ) ( 0.0928 MMK ) = ( x MMK ) .
The units cancel out correctly, resulting in MMK.
Therefore, the correct equation is option b: ( 1 USD ) ⋅ ( 1 USD ) ( 45.85 INR ) ⋅ ( 1 INR ) ( 1.507 BDT ) ⋅ ( 1 BDT ) ( 0.0928 MMK ) = ( x MMK )
Explanation
Understanding the Problem We need to find the correct equation to convert US dollars (USD) to Myanma kyat (MMK) given the exchange rates:
1 USD = 45.85 INR (Indian Rupees)
1 INR = 1.507 BDT (Bangladeshi Taka)
1 BDT = 0.0928 MMK (Myanma Kyat)
The conversion should follow this pattern:
( 1 USD ) × USD INR × INR BDT × BDT MMK = x MMK
We need to check each option to see which one correctly sets up this conversion.
Analyzing the Options Let's analyze each option:
a. ( 1 USD ) ( 45.85 DNR ) ( 1 USD ) ⋅ ( 1.507 BDT ) ( 1 DNR ) ( 0.0928 MMMK ) ( 1 BDT ) = ( x MMM )
* This option has USD in the numerator of the first fraction, which is incorrect. It should have INR in the numerator to cancel out the USD.
b. ( 1 USD ) ⋅ ( 1 USD ) ( 45.85 ANR ) ⋅ ( 45.85 INR ) ( 1.507 BDT ) ⋅ ( 1.507 BDT ) ( 0.0928 MMK ) = ( x MMK )
* This option correctly starts with USD and converts to INR, then to BDT, and finally to MMK. Let's verify the units cancel out:
$\text{USD} \times \frac{\text{INR}}{\text{USD}} \times \frac{\text{BDT}}{\text{INR}} \times \frac{\text{MMK}}{\text{BDT}} = \text{MMK}$
* The units cancel out correctly, so this option is likely correct.
c. ( 1 USD ) ⋅ ( 1 USD ) ( 45.85/ DVR ) ⋅ ( 1 DVR ) ( 1.507 BDT ) ⋅ ( 1 BDT ) ( 0.0928 MMK ) − ( x MMK )
* This option has DVR, which is not a defined currency. Also, the subtraction at the end is incorrect.
d. ( 1 USD ) ⋅ ( 45.85 DVR ) ( 1 USD ) ⋅ ( 1.507 BDT ) ( 45.85 INR ) ⋅ ( 0.0928 MMMK ) ( 1.507 BDT ) = ( x MMK )
* This option has USD in the numerator of the second fraction, which is incorrect. It also has DVR, which is not a defined currency, and MMMK in the denominator of the last fraction, which is inverted.
Conclusion Based on the analysis, option b is the only one that correctly sets up the conversion from USD to MMK:
( 1 USD ) ⋅ ( 1 USD ) ( 45.85 INR ) ⋅ ( 1 INR ) ( 1.507 BDT ) ⋅ ( 1 BDT ) ( 0.0928 MMK ) = ( x MMK )
Examples
Currency conversion is a practical application of math that we use every day when traveling or shopping online from international vendors. For example, if you are planning a trip from the United States to Myanmar, you would need to convert US dollars into Myanma Kyats to understand how much things will cost. The correct setup ensures that you multiply by the correct exchange rates in the correct order, allowing you to accurately determine the equivalent value in the local currency. This is crucial for budgeting and making informed financial decisions while abroad.
