**Questions**

- Solve the simultaneous equation (3 mks)

2x − y = 3

x2 − xy = -4 - A Kenyan businessman US$100 to a company in the United States of America. The Kenyan can either pay through his account in Kenya or through his account in the United Kingdom. Which method is cheaper and by how much? Give your answer in Kenya shillings given that;

1 US dollar = 76.84 Kenya shillings

1 Sterling Pound = 1.53 US dollars

1 Sterling pound = 115.70 Kenya shillings - Foreign exchange on 27/5/2010 was given as follows:

Currency Buying (Kshs) Selling (Kshs) 1 Euro 84.15 84.26 1 Sterling pound 118.35 121.47 - A Kenyan football fan visited South Africa from Kenya. He changed his currency from Kenya shillings to South African rand. The exchange rates in Kenya were as per the table below:-

Buying Selling 9.9399 10.0166 - A French tourist changes 3000 Francs into Kenyan shillings at 1 Franc = Kshs.1.89. He spends shs.4695, then exchanges the remaining shillings back into Francs at 1 Franc =1.95. How many Francs does he receive?
- Hamisi arrived in Nairobi from USA with 40 travelers cheques each with 75 US dollars. How much does she receive in Kshs from the bank on a day when 1 US dollar was equivalent to Kshs 81.40 and the bank charges commission at the rate of Kshs.100 per travelers cheque
- A Kenya bank buys and sells foreign currencies as shown below

Buying in Kshs. Selling in Kshs. 1 Hong Kong dollar 9.74 9.77 1 South African Rand 12.03 12.11 - A Japanese tourist entered Kenya with Kshs.500,000 Japanese Yen which he converted to Kenya currency. While in Kenya, he spend Kshs.16200 in all. He then converted all the remaining money into Euros before leaving for Italy. If he carried out all his transactions at the Stanbic bank using rates shown below, calculate to the nearest Euro, how much money he left Kenya with.
**(****Do not use mathematical tables for this question)**Selling (Kshs.) Buying (Kshs. 100 Jpanese Yen 66.35 66.05 1 Euro 78.15 77.85 - Do not use mathematical tables in this question. Equity bank buys and sells foreign currencies as shown:-

Buying (Kshs.) Selling (Kshs.) 1 US dollar 77.43 78.10 1 South African Rand 9.03 9.51 - A tourist arriving from Britain had UK ₤ 9000. He converted the pounds to Kenyan shillings at a commission of 5%. While in Kenya he spent ¾ of his money. He exchanged the remaining to US dollars with no commission. Calculate to the nearest US dollars the amount using the exchange rate below.

Currency Buying Kshs. Selling Kshs. 1 US dollar

1 UK dollar63.00

125.3063.20

125.95 - A company was to import goods worth Kshs.100,000 from U.K and changed the money to Sterling pounds. The company later realized that it was cheaper to import the same goods from U.S.A and changed the sterling pounds to dollar. Unfortunately the transaction failed and the money was converted to Kenya shillings. How much money did the company end-up with, given that;

1 US dollar = Kshs.78

1 Sterling pound = Kshs.120

1 Sterling pound = 1.79 U.S dollar - A tourist arrives in Kenya from England with S.£ 50,000 and uses the money to buy Kenya shillings. He quickly changes his mind and sells the Kenya shillings to get back his S.£. How much money in S.£ did he get? Use the table below

Buying Selling 1 Sterling pound 120.7131 120.9294 - A Kenyan bank buys and sells foreign currencies at the exchange rates shown below:

Buying (Kshs.) Selling (Kshs.) 1 Euro 147.86 148.00 1 US dollar 74.22 74.50 - Simplify;
- 6a − 2b + 7a − 4b + 2
^{(2x }^{– 2)}/_{2x}−^{(3}^{x }^{+ 2)}/_{4x}

**Answers**

- 2x − y =3

x^{2}− xy = −4

2x − 3 = y

x^{2}− x(2x − 3) = −4

x^{2 }− 2x^{2}+ 3x = −4

−2x^{2}+ 5x+4 = 0

using quadratic equation

= −b ± √(b^{2}− 4ac)/_{2a}= −5 ± √(5^{2}− 4×−2 ×4)/_{2×4}x= −^{2.5}/_{4}or^{12.5}/_{4}The one that satisfies the equation is x =^{12.5}/_{4}therefore substituting in 2x − y = 3 we get y= 3.25 - Through a/c in Kenya

1000000 X 76.84 = Shs.7684000

through a/c in UK^{1000000}/_{1.53}X 115.70 = Shs.7,562,091.15

Through UK less by

768400 – 7562091.85 = 121,908.85 - 6000 turn ______ 6000 X 84.15

= Kshs.504900

Balance = 504900 – 300000

= 204900

჻ sterling pound =^{204900 }/_{121.47}

= 1686.8 - In Rand =
^{2800265}/_{10.0166}= 279562.4264

Expenses = (115,700 + 97000 + 53689)

= 266389 Rand

Remainder = 279562.4264^{266,389.000}/_{13,174.4264}

Amount in Kshs. = 13174.4264 x 9.9399

= 130,942.50 - Kshs. (3000 x 1.89) = 5670

Remain = 5670 – 4695 = 75

Francs =^{(975)}/_{1.95}= 500 - Amount in dollars = 75 x 40 = 3,000

Amount in Ksh = 3000 x 81.40 = 244,200/=

Less commission 4,000

Total received sh 240,200 - Hong Kong 8105,000 x 9.74 = ksh.1022700

Amount spent in Kenya = 403879

Balance = 1,022,600 – 403,879 = 618,821

Amount in South Africa =^{618821}/_{12.11}= 51100rands - 500000
_{J}yen into Kshs.=^{(500000 x 66.5)}/_{100}

= Kshs. 330,250

Amount spend in Kenya= Kshs. 16200

Remained with Kshs. (330250 – 16200)

= Kshs. 314,040

Kshs. 314040 into Euros:

= (314040)

78.15

= 4,018.554063Euros

He left Kenya with = 4,019 Euros (nearest Euro - 1 $ Kshs. 77.43

5600$ = (5600 x 77.43)

= 433608

Spent 201,367

Remainder = (433608 – 201367)

= 232241

1SR shs.9.51

Shs.232241

1 x 232241

9.51

= shs.24420.715 - 1UK ₤ = 125.30

9000 UK ₤ = 125.30 x 9000

= 1,127,700

Commission = 5/100 x 1,127,700 = 56,385

He got 1,071,315

Expenditure = ¾ of 1,071,315 = 803,486.25

Amt. left = 267,828.75

In US $ = 267,828.75

63.20

= 4237.7966 ≃ 4237 US $ - 1 sterling pound = Kshs.120

? = Kshs.100000

100000/120 = 833.3 sterling pounds

1 sterling pound = 1.79 U.S dollars

132

833.3 = ?

= 833.3 x 1.79 = 1491.7 dollars

1 U.S dollar = Kshs.78

1491.7 dollars = Kshs?

1491.7 x 78 = 116350 Kenya shillings- Amount received in Kenya shillings

= Σ50,000 x Shs.120.7131

Σ = Kshs.6035655

Amount received in sterling pound

=^{1Σ}^{}^{x Kshs.6035655}/_{120.9294}

= Σ 49910.568 - Sh(20000 x 147.86) = sh.2957200

To US Dollars = 44700

74.5 = 6000

He received 6000 US Dollars - 6a + 7a – 2b – 4b + 2

= 13a – 6b + 2 ^{2x – 2}/_{2x}–^{(3x + 2)}/_{4x}=^{[2(2x – 2) – (3x + 2)]}/_{4x}

=^{(4x – 3x – 4 – 2)}/_{4x}

=^{x – 6}/_{4x}_{ }

- 6a + 7a – 2b – 4b + 2

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