Simultaneous linear equations: DHS 2024 Promo Q1

Dunman High School2024 PromoPromo P2 Q1●●○ Standard4 marks

What this question tests

System of Linear Equations.

Question

. The selling price of a desktop monitor, keyboard and mouse is $317.90 in total. During the Great Electronics Sale, two companies, $A$ and $B$ , offered the following discounts to their customers.

Company	Discounts given for each item			Total price after
	Desktop monitor	Keyboard	Mouse	the discount
$A$	$10\%$	$15\%$	$10\%$	$282.66
$B$	$5\%$	$25\%$	$20\%$	$283.72

Find the selling prices of a desktop monitor, keyboard and mouse. [3]
Kim works at Company $B$ and the employees from Company $B$ are offered a further $2\%$ discount on the original price of the mouse. Explain if this additional discount will make it more attractive for Kim to purchase all the three items from her own company than from Company $A$ . [1]

Show full worked solution▾

Let the price of a desktop monitor, keyboard and mouse be $x, $y and $z respectively. $\begin{aligned} x+y+z&=317.90\\ 0.9x+0.85y+0.9z&=282.66\\ 0.95x+0.75y+0.8z&=283.72\\ \underline{x=219,\ y=69,\ z=29.9} \end{aligned}$

Employees of Company B will pay $[0.95(219)+0.75(69)+0.78(29.9)] = $283.12 $>$ $282.66.

No, it will not be more attractive for employees from Company B to purchase all the three items from their own company since they will still have to pay more than the sale by Company A .

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