10. (10 points) During the Spring Festival promotion, customers receive a 50 yuan voucher for every 100 yuan paid in cash. These vouchers cannot be exchanged for cash but can be used to purchase goods, with the following rules: vouchers received in a single purchase cannot be used in the same purchase; the cash paid for each purchase must be at least half the value of the goods purchased. Aunt Li has no more than 1550 yuan in cash. Can she buy goods worth 2300 yuan? If yes, design a shopping plan for her; if not, explain the reason.
【Analysis】First, let's see how many coupons 1550 can get at most, which is $1500 \div 2=750$. And $2300=1550+750$ is exactly right, meaning that 1550 cash must be used together with all the 750 coupons to buy goods worth 2300. How can we use both the coupons and cash together? By considering the last purchase, we can easily draw a conclusion. After analysis, if the last purchase is 100 or more than 150, it is impossible to buy goods worth 2300, because the coupons obtained later cannot be used alone, and the problem requires that coupons must be used together with cash. Therefore, to buy goods worth 2300, the last purchase must be 50 cash + 50 coupons (why 50 coupons, not 100 coupons, is also required by the problem, as the cash must not be less than half of the value of the goods). From 50 coupons, we can infer that the previous purchase's cash was 100, and the coupons used together must also be 100. Thus, the reasoning goes as follows:
50+50 (coupons)
$100+100$ (coupons)
200+200 (coupons)
$400+400$ (coupons)
800
On the left is cash $800+400+200+100+50=1550$ yuan, and on the right is coupons $400+200+100+50=750$ yuan. This way, the value of the goods that can be bought is $1550+750=2300$ yuan, so it is possible to buy. According to this, we can solve the problem.

【Solution】According to the problem:
(1) Since the coupons obtained from the last purchase cannot be used, as 1500 yuan is needed to get 750 yuan worth of coupons, the last purchase can use at most 50 yuan in cash;
(2) To use as many coupons as possible, try to use half of the coupons each time, and the coupons used each time are obtained from the previous purchase;
(3) The first purchase can only use cash.
Thus, the last purchase uses 50 yuan in cash and 50 yuan in coupons;
The second-to-last purchase uses 100 yuan in cash and 100 yuan in coupons;
The third-to-last purchase uses 200 yuan in cash and 200 yuan in coupons;
The fourth-to-last purchase uses 400 yuan in cash and 400 yuan in coupons;
The fifth-to-last purchase uses 800 yuan in cash.
The solution that meets the conditions is:
The first purchase uses 800 yuan in cash;
The second purchase uses 400 yuan in cash and 400 yuan in coupons;
The third purchase uses 200 yuan in cash and 200 yuan in coupons;
The fourth purchase uses 100 yuan in cash and 100 yuan in coupons;
The fifth purchase uses 50 yuan in cash and 50 yuan in coupons.
In total: $800+400+400+200+200+100+100+50+50=2300$ (yuan)
Therefore, with no more than 1550 yuan in cash, she can buy goods worth 2300 yuan.