“双十一”期间某购物平台推出优惠活动如下：每满300元可减50元、每满200元可减30元，若付款金额满3500
元还可使用一张280元代金券，满减和代金券可同时享有。已知小张购买了一台洗衣机最终支付3390元，若已
享受最大优惠，则在活动期间购买这台洗衣机相当于在原价基础上约打了几折？

我们可以通过以下步骤计算小张相当于打了几折：

### 1. 设洗衣机的原价为 \( P \) 元。

### 2. 确定小张享受的优惠：
- 小张享受了“每满300元减50元”和“每满200元减30元”的满减活动。
- 满减后的金额满足使用代金券条件，因此还享受了一张280元的代金券。

小张最终支付了3390元，已经享受了最大优惠。

### 3. 计算满减优惠：
- 优惠规则为每满300元减50元，即总价格减去 \( \left\lfloor \frac{P}{300} \right\rfloor \times 50 \) 元。
- 另外，每满200元减30元可以一起使用。这里为了最大优惠，考虑的是每满300元减50元的优惠。

### 4. 使用代金券：
当满减后金额满足条件后，小张还使用了一张280元代金券。

### 5. 方程表达：
设原价为 \( P \)，则根据已知条件可建立方程：
\[ P - \left\lfloor \frac{P}{300} \right\rfloor \times 50 - 280 = 3390 \]

我们可以通过这个方程来求解洗衣机的原价 \( P \)。

### 解答:

让我们通过计算来推导原价。It appears that solving the equation directly using symbolic methods is complicated due to the presence of the floor function. Instead, I will attempt a numerical approach to estimate the original price based on the given conditions.

Let me proceed with this method to calculate the original price.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to explain the manual steps to estimate the original price, or answer any other questions related to this problem?

Here are five related questions to explore further:
1. How does the “every 300 yuan deduct 50 yuan” rule apply if the original price is slightly above or below a multiple of 300?
2. Can you determine how much savings are achieved by combining both discount rules?
3. What would the final price be without using the 280-yuan voucher?
4. How would the discounts change if the purchase price was less than 3500 yuan?
5. Is there a maximum possible discount in this promotional scheme?

**Tip**: When solving multi-step problems, it helps to write down all the steps and values to organize the calculations.

双十一期间某购物平台推出优惠活动如下：每满300元可减50元、每满200元可减30元，若付款金额满3500元还可使用一张280元代金券，满减和代金券可同时享有。已知小张购买了一台洗衣机最终支付3390元，若已享受最大优惠，则在活动期间购买这台洗衣机相当于在原价基础上约打了几折？

Explore how to calculate the final price of a washing machine bought during Double 11 promotions, considering both discount rules and a voucher. Learn step-by-step how to use the discount formula P - ⌊P/300⌋ * 50 - 280 = 3390 and solve for the original price. Ideal for high school students studying algebra and discount problems.

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