Let's break down the problem step-by-step to find the solution:
### Part (a)
Calculate the amount of money in Kenyan Shillings that the businessman received after converting 20,730 Euros.
- The exchange rate for converting Euros to Kenyan Shillings (Kshs) is 144.60 (buying rate).
- The amount in Euros is 20,730.
To find the amount received in Kenyan Shillings:
[tex]\[ \text{Amount in Kshs} = \text{Amount in Euros} \times \text{Exchange rate} \][/tex]
[tex]\[ \text{Amount in Kshs} = 20730 \, \text{Euros} \times 144.60 \, \text{Kshs/Euro} = 2,997,558 \, \text{Kshs} \][/tex]
So, the businessman received 2,997,558 Kenyan Shillings.
### Part (b)
Calculate the amount of money in US Dollars, to the nearest US Dollar, that the businessman received after spending part of the Kenyan Shillings in Kenya.
- The businessman spent 2,410,300 Kenyan Shillings.
- The remaining amount in Kenyan Shillings needs to be converted to US Dollars.
- The exchange rate for converting Kenyan Shillings to US Dollars (buying rate) is 133.40 Kshs/USD.
First, find the remaining amount of Kenyan Shillings after spending:
[tex]\[ \text{Remaining Kshs} = \text{Total amount in Kshs} - \text{Amount spent} \][/tex]
[tex]\[ \text{Remaining Kshs} = 2,997,558 \, \text{Kshs} - 2,410,300 \, \text{Kshs} = 587,258 \, \text{Kshs} \][/tex]
Next, convert the remaining Kenyan Shillings to US Dollars:
[tex]\[ \text{Amount in USD} = \frac{\text{Remaining Kshs}}{\text{Exchange rate}} \][/tex]
[tex]\[ \text{Amount in USD} = \frac{587258 \, \text{Kshs}}{133.40 \, \text{Kshs/USD}} = 4402.23388305847 \, \text{USD} \][/tex]
Rounding to the nearest US Dollar:
[tex]\[ \text{Amount in USD (Rounded)} = 4402 \, \text{USD} \][/tex]
Therefore, the amount of money the businessman received in US Dollars, to the nearest US Dollar, is 4,402 USD.
