Question

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})} \frac{(1 \text{ inr})}{(1.507 \text{ bdt})} \frac{(1 \text{ bdt})}{(0.0928 \text{ mmk})} = (x \text{ mmk})\\)
b. \\((1 \text{ usd}) \frac{(45.85 \text{ inr})}{(1 \text{ usd})} \frac{(1.507 \text{ bdt})}{(45.85 \text{ inr})} \frac{(0.0928 \text{ mmk})}{(1.507 \text{ bdt})} = (x \text{ mmk})\\)
c. \\((1 \text{ usd}) \frac{(45.85 \text{ inr})}{(1 \text{ usd})} \frac{(1.507 \text{ bdt})}{(1 \text{ inr})} \frac{(0.0928 \text{ mmk})}{(1 \text{ bdt})} = (x \text{ mmk})\\)
d. \\((1 \text{ usd}) \frac{(1 \text{ usd})}{(45.85 \text{ inr})} \frac{(45.85 \text{ inr})}{(1.507 \text{ bdt})} \frac{(1.507 \text{ bdt})}{(0.0928 \text{ mmk})} = (x \text{ mmk})\\)

Explanation:

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<reasoning>

Identify conversion factors

Using the Currency Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} &1\text{ USD} = 45.85\text{ INR} \implies \frac{45.85\text{ INR}}{1\text{ USD}} = 1\\ &1\text{ INR} = 1.507\text{ BDT} \implies \frac{1.507\text{ BDT}}{1\text{ INR}} = 1\\ &1\text{ BDT} = 0.0928\text{ MMK} \implies \frac{0.0928\text{ MMK}}{1\text{ BDT}} = 1 \end{aligned}$$

\]

Set up dimensional analysis

Using the Dimensional Analysis knowledge point
\[
(1\text{ USD}) \cdot \frac{(45.85\text{ INR})}{(1\text{ USD})} \cdot \frac{(1.507\text{ BDT})}{(1\text{ INR})} \cdot \frac{(0.0928\text{ MMK})}{(1\text{ BDT})} = (x\text{ MMK})
\]
</reasoning>

<answer>
<mcq-option>a. \((1\text{USD}) \frac{(1\text{USD})}{(45.85\text{INR})} \frac{(1\text{INR})}{(1.507\text{BDT})} \frac{(1\text{BDT})}{(0.0928\text{MMK})} = (x\text{MMK})\)</mcq-option>
<mcq-option>b. \((1\text{USD}) \frac{(45.85\text{INR})}{(1\text{USD})} \frac{(1.507\text{BDT})}{(45.85\text{INR})} \frac{(0.0928\text{MMK})}{(1.507\text{BDT})} = (x\text{MMK})\)</mcq-option>
<mcq-correct>c. \((1\text{USD}) \frac{(45.85\text{INR})}{(1\text{USD})} \frac{(1.507\text{BDT})}{(1\text{INR})} \frac{(0.0928\text{MMK})}{(1\text{BDT})} = (x\text{MMK})\)</mcq-correct>
<mcq-option>d. \((1\text{USD}) \frac{(1\text{USD})}{(45.85\text{INR})} \frac{(45.85\text{INR})}{(1.507\text{BDT})} \frac{(1.507\text{BDT})}{(0.0928\text{MMK})} = (x\text{MMK})\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify conversion factors

Using the Currency Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} &1\text{ USD} = 45.85\text{ INR} \implies \frac{45.85\text{ INR}}{1\text{ USD}} = 1\\ &1\text{ INR} = 1.507\text{ BDT} \implies \frac{1.507\text{ BDT}}{1\text{ INR}} = 1\\ &1\text{ BDT} = 0.0928\text{ MMK} \implies \frac{0.0928\text{ MMK}}{1\text{ BDT}} = 1 \end{aligned}$$

\]

Set up dimensional analysis

Using the Dimensional Analysis knowledge point
\[
(1\text{ USD}) \cdot \frac{(45.85\text{ INR})}{(1\text{ USD})} \cdot \frac{(1.507\text{ BDT})}{(1\text{ INR})} \cdot \frac{(0.0928\text{ MMK})}{(1\text{ BDT})} = (x\text{ MMK})
\]
</reasoning>

<answer>
<mcq-option>a. \((1\text{USD}) \frac{(1\text{USD})}{(45.85\text{INR})} \frac{(1\text{INR})}{(1.507\text{BDT})} \frac{(1\text{BDT})}{(0.0928\text{MMK})} = (x\text{MMK})\)</mcq-option>
<mcq-option>b. \((1\text{USD}) \frac{(45.85\text{INR})}{(1\text{USD})} \frac{(1.507\text{BDT})}{(45.85\text{INR})} \frac{(0.0928\text{MMK})}{(1.507\text{BDT})} = (x\text{MMK})\)</mcq-option>
<mcq-correct>c. \((1\text{USD}) \frac{(45.85\text{INR})}{(1\text{USD})} \frac{(1.507\text{BDT})}{(1\text{INR})} \frac{(0.0928\text{MMK})}{(1\text{BDT})} = (x\text{MMK})\)</mcq-correct>
<mcq-option>d. \((1\text{USD}) \frac{(1\text{USD})}{(45.85\text{INR})} \frac{(45.85\text{INR})}{(1.507\text{BDT})} \frac{(1.507\text{BDT})}{(0.0928\text{MMK})} = (x\text{MMK})\)</mcq-option>
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