百佳（Payprice）超市在“生鲜角”举行了促销活动。Ng 女士、Lim 女士、Yeo 先生和 Heng 太太参加了本次百佳超市的促销活动。由于商品没有预先包装，顾客需按所选海鲜的重量付费。他们购买的海鲜重量汇总于下表：

	Ng 女士	Lim 女士	Yeo 先生	Heng 太太
乌贼 (kg)	0.75	0.60	1.30	1.10
日本鲈鱼 (kg)	1.20	1.45	0.90	1.80
老虎虾 (kg)	0.20	0.45	0.50	0.30

Ng 女士、Lim 女士和 Yeo 先生分别支付了 $28.51、$35.79 和 $33.40。Heng 太太发现她身上只有 $50。判断她是否有足够的钱来支付她所购买的商品。

1. Formulate a system of linear equations based on the purchase records.

Let $x$, $y$, and $z$ be the price per kg of Cuttlefish, Japanese Sea Bass, and Tiger Prawns respectively.

From the table, we set up the following equations based on the amounts paid:

2. Solve the system of equations using a graphing calculator.

Using a graphing calculator to solve the system, we obtain:
$x = 7.8$
$y = 15.9$
$z = 17.9$

The unit prices are $\char36{}7.80/\text{kg}$ for Cuttlefish, $\char36{}15.90/\text{kg}$ for Japanese Sea Bass, and $\char36{}17.90/\text{kg}$ for Tiger Prawns.

3. Calculate the total cost of Mrs Heng's purchase.

Total cost for Mrs Heng $= 1.10x + 1.80y + 0.30z$
$= 1.10(7.80) + 1.80(15.90) + 0.30(17.90)$
$= 8.58 + 28.62 + 5.37$
$= 42.57$

4. Compare the cost to the amount of money Mrs Heng has to draw a conclusion.

Mrs Heng has $\char36{}50$.
Since $\char36{}42.57 \le \char36{}50$, she has enough money to pay for her purchase.