Processing math: 100%

SPM Mathematics 2023, Paper 2 – Question 15


Question 15:
 (a) It is given that [72x+34]=[75y14]

Determine the value of x and of y. [2 marks]

(b) A supermarket sells boxes of sushi and pieces of fried chicken.
(i) Lily spent RM55 on 3 boxes of sushi and 2 pieces of fried chicken. Kelly spent RM20 more compared to Lily on 4 boxes of sushi and 3 pieces of fried chicken. Using matrix method, calculate the price of a box of sushi and of a piece of fried chicken. [5 marks] 


(ii) Diagram 9 shows the discounts given by the supermarket on a particular day.


Jane has RM50. She wants to buy 2 boxes of sushi and 8 pieces of fried chicken. Does she have enough money to buy these items at the discounted price? Justify your answer by using matrix multiplication. [3 marks]


Solution:
(a)
[72x+34]=[75y14]x+3=1x=45y=2y=25

(b)(i)
3x+2y=55 (Lily) 4x+3y=55+20 (Kelly) 4x+3y=75
[3243][xy]=[5575][xy]=1(3)(3)(2)(4)[3243][5575][xy]=[(3×55)+(2×75)(4×55)+(3×75)][xy]=[165150220+225][xy]=[155] A box of sushi = RM15  A piece of fried chicken = RM5 

(b)(ii)
 A box of sushi at discounted price =15×80100= RM12 
 A piece of fried chicken at discounted price =5×60100= RM3 
2 boxes of sushi and 8 pieces of fried chicken in matrix multiplication =[28][123]=[2×12+8×3]=[48]
 Therefore, Jane has enough money as only RM48 is needed. 

Leave a Comment