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13. A Kenyan bank buys and sells foreign currency as shown below.

\begin{tabular}{|l|l|l|}
\cline { 2 - 3 } \multicolumn{1}{c|}{} & Buying Ksh & Selling Ksh \\
\hline 1 US dollar & 103.00 & 106.20 \\
\hline
\end{tabular}
\begin{tabular}{|l|l|l|}
\hline \[tex]$(\$[/tex]) & & \\
\hline \begin{tabular}{l}
1 UK pound \\
(£)
\end{tabular} & 145.00 & 149.95 \\
\hline
\end{tabular}

A tourist arrived in Kenya with £9600, which he converted into Ksh at a commission of 5%. He later used [tex]$\frac{3}{4}$[/tex] of the money before changing the balance to dollars at no commission.

Calculate, to the nearest dollar, the amount he received.

(3 marks)

Sagot :

GinnyAnsweridn
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]
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