一家咖啡馆出售三种蛋糕：香蕉、巧克力和核桃。该咖啡馆对购买超过 12 个蛋糕的任何顾客给予总价 12% 的折扣。爱丽丝（Alice）、贝蒂（Betty）和夏洛特（Charlotte）购买的每种蛋糕的数量以及支付的总金额见下表。
香蕉巧克力核桃支付金额 ($)
爱丽丝 5 3 2 52
贝蒂 3 4 5 68
夏洛特 4 8 2 66
确定每种蛋糕的原始售价。

	香蕉	巧克力	核桃	支付金额 ($)
爱丽丝	5	3	2	52
贝蒂	3	4	5	68
夏洛特	4	8	2	66

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Determine whether each customer qualifies for the discount based on the number of cakes bought.

Total cakes bought by each customer:

2. Define variables and set up the system of linear equations.

Let $x$ , $y$ , and $z$ be the original selling prices of banana, chocolate, and walnut cakes respectively.

From Alice's purchase:
$5x + 3y + 2z = 52$

From Betty's purchase:
$3x + 4y + 5z = 68$

From Charlotte's purchase (with a $12\%$ discount, paying $88\%$ ):
$0.88(4x + 8y + 2z) = 66$
$4x + 8y + 2z = \frac{66}{0.88} = 75$

3. Solve the system of equations.

Solving the system of linear equations (using a graphing calculator):
$x = 4.5, \quad y = 5.5, \quad z = 6.5$

The original selling prices are $4.50 for a banana cake, $5.50 for a chocolate cake, and $6.50 for a walnut cake.

答案

Banana cake: $4.50, Chocolate cake: $5.50, Walnut cake: $6.50

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