YIJC Promo 9758/2020/Q1 Four families, namely Chan, Lee, Tan and Wong, purchase masks, hand sanitisers and thermometers at a pharmacy. The Tan family made their purchase using a voucher, which entitled them to a 20% discount off the total amount paid. The quantity of each item purchased and the total amounts paid are shown in the following table.

	Masks (in boxes)	Hand sanitisers	Thermometers	Total Amount paid
Chan	4	6	5	$89.30
Lee	2	4	8	$83.30
Tan	3	5	3	$50.28
Wong	5	2	4

Calculate the total amount the Wong family paid.

1. Define variables and set up the equations for the Chan and Lee families based on their purchases.

Let $x$, $y$, and $z$ be the price of one box of masks, one hand sanitiser, and one thermometer respectively.
From the Chan family's purchase:
$4x + 6y + 5z = 89.30$
From the Lee family's purchase:
$2x + 4y + 8z = 83.30$

2. Formulate the equation for the Tan family, accounting for the 20% discount.

The Tan family received a $20\%$ discount, which means they paid $80\%$ of the original total amount. Therefore:
$0.80(3x + 5y + 3z) = 50.28$
$3x + 5y + 3z = \frac{50.28}{0.80}$
$3x + 5y + 3z = 62.85$

3. Solve the system of linear equations to find the unit prices.

Using a graphing calculator (GC) to solve the system of three linear equations, we obtain:
$x = 11.25$
$y = 1.80$
$z = 6.70$

4. Calculate the total amount paid by the Wong family.

The amount paid by the Wong family is $5x + 2y + 4z$:
$5(11.25) + 2(1.80) + 4(6.70)$
$= 56.25 + 3.60 + 26.80$
$= 86.65$