YIJC Promo 9758/2020/Q1 Chan、Lee、Tan 和 Wong 四个家庭在药房购买了口罩、洗手液和体温计。Tan 家庭使用了代金券进行购买，该代金券使他们享受了总支付金额 20% 的折扣。每个家庭购买的每种商品的数量以及总支付金额如下表所示。

	口罩（盒）	洗手液	体温计	总支付金额
Chan	4	6	5	$89.30
Lee	2	4	8	$83.30
Tan	3	5	3	$50.28
Wong	5	2	4

计算 Wong 家庭支付的总金额。

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 $5x + 2y + 4z$:
$5(11.25) + 2(1.80) + 4(6.70)$
$= 56.25 + 3.60 + 26.80$
$= 86.65$