Page 22 - Top Class F5 - Mathematics (Chapter 2)

Mathematics Form 5 Chapter 2 Matrices

29. Solve the following problems. PL 5 Daily Application
Selesaikan masalah berikut.

(a) Two machines, P and Q, in a factory can produce 80 bulbs in one minute. If machine P operates for
2 minutes and machine Q operates for 5 minutes, 310 bulbs can be produced. It is given that the machine
P and machine Q can produce p bulbs and q bulbs in one minute respectively.
Dua mesin, P dan Q, di sebuah kilang dapat menghasilkan 80 biji mentol dalam masa seminit. Jika mesin P beroperasi selama
2 minit dan mesin Q beroperasi selama 5 minit, 310 biji mentol dapat dihasilkan. Diberi bahawa mesin P dan mesin Q masing-
masing dapat menghasilkan p biji mentol dan q biji mentol dalam masa seminit.
(i) Write two linear equations in terms of p and q to represent the above information.
Tuliskan dua persamaan linear dalam sebutan p dan q untuk mewakili maklumat di atas.
(ii) Hence, by using matrix method, find the value of p and of q.
Seterusnya, dengan menggunakan kaedah matriks, cari nilai p dan nilai q.
(i) p + q = 80     
80
1 1 p
2p + 5q = 310 (ii) 2 5 q = 310
p
  = 1(5) – 1(2) –2 1 310

5 –1 80
 
1
q
1 400 – 310
=  
3 –160 + 310
1 90
=  
3 150
 
30
= 50
Hence / Maka, p = 30, q = 50
(b) Mr Tan wants to invest in Fund X and Fund Y. It is given that Fund X gives a dividend of 5% per
annum while Fund Y gives a dividend of 12% per annum. Mr Tan’s investment in Fund X is RM5 000
less than his investment in Fund Y. Mr Tan invests RMx into Fund X and RMy into Fund Y to earn a
total dividend of RM1 025 per annum.
Encik Tan hendak membuat pelaburan ke Dana X dan Dana Y. Diberi bahawa Dana X memberikan dividen sebanyak 5%
setahun manakala Dana Y memberikan dividen sebanyak 12% setahun. Pelaburan Encik Tan ke Dana X adalah RM5 000
kurang daripada pelaburan ke Dana Y. Encik Tan melabur RMx ke Dana X dan RMy ke Dana Y untuk mendapat jumlah dividen
sebanyak RM1 025 setahun.
(i) Write two linear equations in terms of x and y to represent the above information.
Tuliskan dua persamaan linear dalam sebutan x dan y untuk mewakili maklumat di atas.
(ii) Hence, by using matrix method, find the value of x and of y.
Seterusnya, dengan menggunakan kaedah matriks, cari nilai x dan nilai y.

(i) 0.05x + 0.12y = 1 025 ⇒ 5x + 12y = 102 500
y – x = 5 000 ⇒ x – y = –5 000
  
 5 12 x 102500 
(ii) 1 –1 y = –5000
x
  = 5(–1) – 12(1) –1 5  –5000 
–1 –12 102500

1
y
1 –102500 + 60000
= –  
17 –102500 – 25000
1 –42500
= –  
17 –127500
 2500 
= 7500
Hence / Maka, x = 2 500, y = 7 500

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