Let's solve this step-by-step, taking into consideration the given constraints:
### Step 1: Convert £9600 into Kshs with a 5% commission
First, we need to find out how much Kshs the tourist would get from converting £9600 into Kenyan shillings (Kshs) at the given buying rate. The buying rate for 1 UK pound is Ksh 145.00.
[tex]\[
9600 \, \text{pounds} \times 145 = 1392000 \, \text{Ksh}
\][/tex]
Next, we calculate the commission amount. The commission rate is 5%, so the commission amount is:
[tex]\[
1392000 \, \text{Ksh} \times 0.05 = 69600 \, \text{Ksh}
\][/tex]
We subtract the commission amount from the total to get the amount in Kshs after the commission:
[tex]\[
1392000 \, \text{Ksh} - 69600 \, \text{Ksh} = 1322400 \, \text{Ksh}
\][/tex]
### Step 2: Tourist uses 3/8 of the money
The tourist used [tex]\(\frac{3}{8}\)[/tex] of the money. So, we need to find out how much he used:
[tex]\[
1322400 \, \text{Ksh} \times \left(\frac{3}{8}\right) = 495900 \, \text{Ksh}
\][/tex]
### Step 3: Calculate the remaining amount in Kshs
Subtract the used amount from the initial amount after commission to find the balance:
[tex]\[
1322400 \, \text{Ksh} - 495900 \, \text{Ksh} = 826500 \, \text{Ksh}
\][/tex]
### Step 4: Convert the balance in Kshs to dollars
Finally, we convert the remaining Kshs into dollars at the given selling rate, which is Ksh 149.95 for 1 UK pound. Since we're asked to find the amount in dollars, we'll use the selling rate for dollars:
[tex]\[
826500 \, \text{Ksh} \div 149.95 = 5512.17 \, \text{dollars}
\][/tex]
We round this amount to the nearest dollar:
[tex]\[
\approx 5512 \, \text{dollars}
\][/tex]
Therefore, the amount he received in dollars is:
[tex]\[
\boxed{5512 \, \text{dollars}}
\][/tex] to the nearest dollar.
