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4. The matrix below describes the price of [tex][tex]$1 \text{ kg}$[/tex][/tex] of four items in Bhutan in ngultrums. Use matrix multiplication to show the prices in United States (U.S.) dollars in a matrix. (Use the exchange rate, 1 U.S. dollar = Nu 63.5)

Beef, Cheese, Rice, Flour
[tex]\[
P = \left[\begin{array}{llll}
80 & 280 & 25 & 16
\end{array}\right]
\][/tex]



Answer :

GinnyAnswer
To find the prices of the four items (Beef, Cheese, Rice, and Flour) in U.S. dollars, we first need to use the given exchange rate, where 1 U.S. dollar equals 63.5 ngultrums.

Given the matrix of prices in ngultrums, [tex]\( P \)[/tex]:

[tex]\[ P = \begin{bmatrix} 80 & 280 & 25 & 16 \end{bmatrix} \][/tex]

And the exchange rate:

[tex]\[ \text{Exchange Rate} = \frac{1 \text{ USD}}{63.5 \text{ NGN}} \approx 0.015748 \][/tex]

To convert the prices from ngultrums to U.S. dollars, we multiply each element in the matrix [tex]\( P \)[/tex] by the exchange rate.

Let's do the conversion step-by-step for each item.

1. Beef:

[tex]\[ \text{Price of Beef in USD} = 80 \text{ ngultrums} \times 0.015748 \text{ USD/ngultrum} \approx 1.25984252 \text{ USD} \][/tex]

2. Cheese:

[tex]\[ \text{Price of Cheese in USD} = 280 \text{ ngultrums} \times 0.015748 \text{ USD/ngultrum} \approx 4.40944882 \text{ USD} \][/tex]

3. Rice:

[tex]\[ \text{Price of Rice in USD} = 25 \text{ ngultrums} \times 0.015748 \text{ USD/ngultrum} \approx 0.39370079 \text{ USD} \][/tex]

4. Flour:

[tex]\[ \text{Price of Flour in USD} = 16 \text{ ngultrums} \times 0.015748 \text{ USD/ngultrum} \approx 0.25196850 \text{ USD} \][/tex]

After converting each price, we can form the final matrix of prices in U.S. dollars:

[tex]\[ P_{USD} = \begin{bmatrix} 1.25984252 & 4.40944882 & 0.39370079 & 0.25196850 \end{bmatrix} \][/tex]

This matrix represents the prices of 1 kg of Beef, Cheese, Rice, and Flour converted from ngultrums to U.S. dollars using the given exchange rate.

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