Page 54 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 3 Sistem Persamaan

Katakan / Let Gantikan p = 20 ke dalam d / Substitute p = 20 into d
p = bilangan kek P / the number of cake P 20 + r = 100
q = bilangan kek Q / the number of cake Q r = 80
r = bilangan kek R / the number of cake R
Gantikan p = 20 dan r = 80 ke dalam 
0.2p + 0.4q + 0.3r = 30 ................. Substitute p = 20 and r = 80 into 
0.3p + 0.4q + 0.4r = 40 .................b 0.2(20) + 0.4q + 0.3(80) = 30
0.5p + 0.2q + 0.3r = 35 .................c q = 5
b − : 0.1p + 0.1r = 10 Bilangan kek yang boleh dibuat ialah 20 biji kek P,
p + r = 100 ....................d 5 biji kek Q dan 80 biji kek R.
The number of cakes that can be made of cake P is 20, cake Q is 5
c × 2: p + 0.4q + 0.6r = 70 ..................e and cake R is 80.
e − b: 0.7p + 0.2r = 30
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7p + 2r = 300 ...............f
d × 2: 2p + 2r = 200 .............................g
f − g: 5p = 100
p = 20

(b) Tiga buah bank, X, Y dan Z menawarkan kadar faedah simpanan masing-masing 3%, 5% dan 4.5%
setahun. Encik Jiang telah menyimpan wangnya dengan jumlah yang berbeza dalam ketiga-tiga
bank itu. Jumlah wang simpanan dalam bank X ialah dua kali jumlah wang simpanan dalam bank Y.
Jumlah wang simpanan Encik Jiang ialah RM14 000 dan jumlah faedah yang diperolehnya bagi tempoh
setahun daripada ketiga-tiga bank itu ialah RM555. Cari jumlah wang yang disimpan oleh Encik Jiang
dalam setiap bank itu. TP5
Three banks X, Y and Z offer the interest rate of savings at 3%, 5% and 4.5% per year respectively. Mr Jiang has saved his money with
different amounts in the three banks. The savings amount in bank X is twice the savings amount in bank Y. Mr Jiang’s total savings is
RM14 000 and the total amount of interest obtained for one-year period from the three banks is RM555. Find the amount of money
saved by Mr Jiang in each of the banks.

Katakan / Let Gantikan  dan d ke dalam c
x = jumlah simpanan dalam bank X Substitute  and d into c
savings amount in bank X 0.03(2y) + 0.05y + 0.045(14 000 − 3y) = 555
y = jumlah simpanan dalam bank Y 0.06y + 0.05y + 630 − 0.135y = 555
savings amount in bank Y −0.025y = −75
z = jumlah simpanan dalam bank Z y = 3 000
savings amount in bank Z
Gantikan y = 3 000 ke dalam 
x = 2y ............................................................ Substitute y = 3 000 into 
x + y + z = 14 000 .....................................b x = 2(3 000)
0.03x + 0.05y + 0.045z = 555 ...............c = 6 000

Gantikan  ke dalam b / Substitute  into b Gantikan y = 3 000 ke dalam (4)
2y + y + z = 14 000 Substitute y = 3 000 into d
3y + z = 14 000 z = 14 000 − 3(3 000)
z = 14 000 − 3y ...............d = 5 000
Jumlah wang yang disimpan dalam bank X ialah
RM6 000, bank Y ialah RM3 000 dan bank Z ialah
RM5 000.
The amount of money saved in bank X is RM6 000, in bank Y is
RM3 000 and in bank Z is RM5 000.

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