Simultaneous linear equations: DHS 2024 Promo Q1

Dunman High School2024 PromoPromo P1 Q1●○○ Foundational3 marks

What this question tests

Systems of linear equations.

Question

. A café sells three types of cake: banana, chocolate and walnut. The café gives $12\%$ discount on total cost to any customer who buys more than $12$ cakes. The number of each type of cake bought by Alice, Betty and Charlotte, together with the total amount paid, are shown in the following table.

	Banana	Chocolate	Walnut	Amount paid ($)
Alice	5	3	2	52
Betty	3	4	5	68
Charlotte	4	8	2	66

Determine the original selling price of each type of cake. [3]

Show full worked solution▾

Let $b$ , $c$ and $w$ be the original prices of banana, chocolate and walnut cakes respectively. $\begin{aligned} 5b+3c+2w&=52\quad\text{(1)}\\ 3b+4c+5w&=68\quad\text{(2)}\\ 4b+8c+2w&=75\quad\text{(3)} \end{aligned}$ Using GC, $b=4.50,\quad c=5.50\text{ and }w=6.50$

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