SPM Additional Mathematics 2019, Paper 2 (Question 15)

Question 15:
Table 3 shows information related to five cake ingredients J, K, L, M and N used by a baker in his business.

Table 3

The composite index for the cost of making the cakes in the year 2020 based on the year 2016 is 136.
(a)(i) Find the value of x and of y.
(ii) Calculate the price for ingredient M in the year 2016 if the price in the year 2020 is RM6.30.
[4 marks]

(b) Calculate the value of p. [3 marks]

(c) The cost of baking a cake in the year 2016 is RM25.
Find the selling price of a cake made in the year 2020, if the baker intends to make a profit of 80%. [3 marks]

Solution:
(a)(i)

\begin{array}{l} \frac{P_{2018}}{P_{2016}} \times 100 = 115, \\ \frac{P_{2020}}{P_{2018}} \times 100 = 140 \\ x = \frac{P_{2020}}{P_{2016}} \times 100 \\ = \frac{P_{2020}}{P_{2018}} \times \frac{P_{2018}}{P_{2016}} \times 100 \\ = 1.40 \times 115 \\ = 161 \\ y = \frac{P_{2020}}{P_{2016}} \times 100 \\ = \frac{P_{2020}}{P_{2018}} \times \frac{P_{2018}}{P_{2016}} \times 100 \\ = 0.90 \times 140 \\ = 126 \end{array}

$\begin{array}{l} \frac{P_{2018}}{P_{2016}} \times 100 = 115, \\ \frac{P_{2020}}{P_{2018}} \times 100 = 140 \\ x = \frac{P_{2020}}{P_{2016}} \times 100 \\ = \frac{P_{2020}}{P_{2018}} \times \frac{P_{2018}}{P_{2016}} \times 100 \\ = 1.40 \times 115 \\ = 161 \\ y = \frac{P_{2020}}{P_{2016}} \times 100 \\ = \frac{P_{2020}}{P_{2018}} \times \frac{P_{2018}}{P_{2016}} \times 100 \\ = 0.90 \times 140 \\ = 126 \end{array}$

(a)(ii)

\begin{array}{l} For ingredient M, \\ \frac{P_{2020}}{P_{2016}} \times 100 = 126 \\ \frac{RM 6.30}{P_{2016}} \times 100 = 126 \\ P_{2016} = \frac{RM 6.30}{126} \times 100 \\ = RM 5 \end{array}

$\begin{array}{l} For ingredient M, \\ \frac{P_{2020}}{P_{2016}} \times 100 = 126 \\ \frac{RM 6.30}{P_{2016}} \times 100 = 126 \\ P_{2016} = \frac{RM 6.30}{126} \times 100 \\ = RM 5 \end{array}$

(b)

\begin{array}{l} Composite index = 136 \\ \frac{\sum I W}{\sum W} = 136 \\ \frac{(124) (5) + (161) (6) + (130) (p) + (126) (4) + (120) (2)}{5 + 6 + p + 4 + 2} = 136 \\ 130 p + 2330 = 136 (17 + p) \\ 130 p + 2330 = 2312 + 136 p \\ 6 p = 18 \\ p = 3 \end{array}

$\begin{array}{l} Composite index = 136 \\ \frac{\sum I W}{\sum W} = 136 \\ \frac{(124) (5) + (161) (6) + (130) (p) + (126) (4) + (120) (2)}{5 + 6 + p + 4 + 2} = 136 \\ 130 p + 2330 = 136 (17 + p) \\ 130 p + 2330 = 2312 + 136 p \\ 6 p = 18 \\ p = 3 \end{array}$

(c)

\begin{array}{l} Cost price of a cake = RM 25 \times 1.36 \\ = RM 34 \\ Selling price = 180 % \times RM 34 \\ = \frac{180}{100} \times RM 34 \\ = RM61 .20 \end{array}

$\begin{array}{l} Cost price of a cake = RM 25 \times 1.36 \\ = RM 34 \\ Selling price = 180 % \times RM 34 \\ = \frac{180}{100} \times RM 34 \\ = RM61 .20 \end{array}$

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