To determine how much the tomatoes cost in rand per kilogram, follow these steps:
1. Identify the given ratios:
- Cost of tomatoes in dollars per pound: [tex]\(\frac{0.83 \text{ dollars}}{1 \text{ lb}}\)[/tex]
- Conversion factor from pounds to kilograms: [tex]\(\frac{2.2 \text{ lb}}{1 \text{ kg}}\)[/tex]
- Conversion factor from rands to dollars: [tex]\(\frac{0.074 \text{ dollars}}{1 \text{ rand}}\)[/tex]
2. Calculate the cost of tomatoes in dollars per kilogram:
- You initially know the cost is [tex]\(0.83 \text{ dollars per pound}\)[/tex].
- There are [tex]\(2.2\)[/tex] pounds in a kilogram.
- Thus, the cost in dollars per kilogram is:
[tex]\[
\frac{0.83 \text{ dollars}}{1 \text{ lb}} \times \frac{2.2 \text{ lb}}{1 \text{ kg}} = 1.826 \text{ dollars per kilogram}
\][/tex]
3. Convert the price from dollars per kilogram to rand per kilogram:
- We know [tex]\(1 \text{ rand}\)[/tex] is worth [tex]\(0.074 \text{ dollars}\)[/tex].
- Therefore, to convert [tex]\(1.826 \text{ dollars per kilogram}\)[/tex] to rand, divided by [tex]\(0.074 \text{ dollars per rand}\)[/tex]:
[tex]\[
\frac{1.826 \text{ dollars per kilogram}}{0.074 \text{ dollars per rand}} = 24.675675675675677 \text{ rand per kilogram}
\][/tex]
4. Round the final answer to the nearest hundredth:
[tex]\(
24.675675675675677 \text{ rand per kilogram} \approx 24.68 \text{ rand per kilogram}
\)[/tex]
So, the cost of tomatoes in rand per kilogram is [tex]\(\boxed{24.68}\text{ rand per kilogram}\)[/tex].
