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.
