Equations Questions and Answers - Form 1 Topical Mathematics

Questions

1. Solve the simultaneous equation (3 mks)
   2x − y = 3
   x2 − xy = -4
2. 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
3. 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 tourist came to Kenya from London with 6000 Euros which he converted to Kenya shillings at a bank. While in Kenya he spent a total of Kshs.300,000 then converted the balance into sterling pounds at the Same bank. Calculate the amount in sterling pounds he received.
4. 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

   He has a total of shs.2,8000,265 and must spend 13 days. During his stay, he spent 8900 Rands on food and accommodation, 97,000 Rands on a return air ticket and 53689 Rands on entertainment. On his return, he converted the remaining amount into Kshs. How much did he receive to the nearest cents?
5. 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?
6. 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
7. 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 tourist arrived in Kenya with 105,000 Hong Kong dollars and changed the amount to Kenya shillings. While in Kenya, she spent Shs.403,879 and changed the balance to South African rand before leaving for South Africa. Calculate the amount, in South African rand that she received
8. 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

9. 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 arrived in Kenya with 5,600 US dollars and changed the whole amount to Kenya shillings while in Kenya he spend shs.201,367 and changed the balance to South African rand before leaving to S. Africa . Calculate the amount in S. African rand that she received
10. 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 dollar	63.00  125.30	63.20  125.95

11. 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
12. 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

13. 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

    An American arrived in Kenya with 20000 Euros. He converted all the Euros to Kenya shillings at the bank. He spent Kshs.25100 200 while in Kenya and converted the remaining Kenya shillings into US Dollars at the bank. Find the amount in dollars that he received
14. Simplify;
    1. 6a − 2b + 7a − 4b + 2
    2. ^{(2x – 2)}/_2x − ^{(3x + 2)}/_4x

Answers

1. 2x − y =3
   x² − xy = −4
   2x − 3 = y
   x² − x(2x − 3) = −4
   x² − 2x² + 3x = −4
   −2x² + 5x+4 = 0
   using quadratic equation
   = −b ± √(b² − 4ac)/_2a
   = −5 ± √(5² − 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
2. 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
3. 6000 turn ______ 6000 X 84.15
   = Kshs.504900
   Balance = 504900 – 300000
   = 204900
   ჻ sterling pound =²⁰⁴⁹⁰⁰ /_121.47
   = 1686.8
4. 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
5. Kshs. (3000 x 1.89) = 5670
   Remain = 5670 – 4695 = 75
   Francs =⁽⁹⁷⁵⁾/_1.95 = 500
   
6. 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
7. 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
8. 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
9. 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
10. 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 $
11. 1 sterling pound = Kshs.120
    ? = Kshs.100000
    100000/120 = 833.3 sterling pounds
    1 sterling pound = 1.79 U.S dollars
12. 
    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
13. Amount received in Kenya shillings
    = Σ50,000 x Shs.120.7131
    Σ = Kshs.6035655
    Amount received in sterling pound
    = ^{1Σx Kshs.6035655}/_120.9294
    = Σ 49910.568
14. Sh(20000 x 147.86) = sh.2957200
    To US Dollars = 44700
    74.5 = 6000
    He received 6000 US Dollars
15. 1. 6a + 7a – 2b – 4b + 2
       = 13a – 6b + 2
    2. ^{2x – 2}/_2x – ^{(3x + 2)}/_4x = ^{[2(2x – 2) – (3x + 2)]}/_4x
       = ^{(4x – 3x – 4 – 2)}/_4x
       = ^{x – 6}/_4x