Let's solve this problem step by step:
1. Convert Pounds to Kenyan Shillings (Ksh):
First, we need to convert the pounds into Kenyan Shillings using the buying rate.
[tex]\[
\text{Buying rate for 1 pound} = 145 \text{ Ksh}
\][/tex]
The tourist has £9600:
[tex]\[
\text{Amount in Ksh} = 9600 \times 145 = 1,392,000 \text{ Ksh}
\][/tex]
2. Calculate the Commission:
The bank charges a commission of 5% on the conversion.
[tex]\[
\text{Commission rate} = 0.05
\][/tex]
[tex]\[
\text{Commission on 1,392,000 Ksh} = 1,392,000 \times 0.05 = 69,600 \text{ Ksh}
\][/tex]
3. Amount in Ksh After Deducting Commission:
[tex]\[
\text{Amount after commission} = 1,392,000 - 69,600 = 1,322,400 \text{ Ksh}
\][/tex]
4. Calculate the Amount Used:
The tourist spends [tex]\( \frac{3}{4} \)[/tex] of the money:
[tex]\[
\text{Fraction used} = \frac{3}{4}
\][/tex]
[tex]\[
\text{Ksh spent} = 1,322,400 \times \frac{3}{4} = 991,800 \text{ Ksh}
\][/tex]
5. Calculate the Remaining Amount in Ksh:
[tex]\[
\text{Ksh remaining} = 1,322,400 - 991,800 = 330,600 \text{ Ksh}
\][/tex]
6. Convert Remaining Ksh to Dollars:
The tourist converts the remaining Ksh back to Dollars using the selling rate:
[tex]\[
\text{Selling rate for 1 dollar} = 106.20 \text{ Ksh}
\][/tex]
[tex]\[
\text{Dollars received} = \frac{330,600}{149.95} \approx 220.4
\][/tex]
7. Round to the Nearest Dollar:
To find the nearest dollar:
[tex]\[
\text{Rounded dollars} = 220
\][/tex]
Therefore, the amount the tourist received when converting back to dollars, to the nearest dollar, is:
[tex]\[
\boxed{220}
\][/tex]
