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The sixth grade mathematics optimization training book 2
Extended part (20 points)

I. Fill in the blanks (10)

1, A and B are two digits, A is as big as B, and the minimum value of the sum of A and B is ().

2, a piece of cloth for adults, can make 12 sets of clothes, such as children, can make 20 sets of clothes, it is known that adults use 0.8 meters more cloth than children, this cloth * * * has () meters.

3. If the radius of the bottom surface of a cylinder is enlarged by 3 times and the height by 2 times, its bottom area will be enlarged by () times, lateral area by () times and volume by () times.

4. The length of rectangle is12cm. If its width is extended, it becomes a square. It turns out that the width of this rectangle is () cm and the area is () cm 2.

Hospital experiment situation

200 people in Zhongshan Hospital tried it, and 150 people were effective.

40 people in Pok Oi Hospital tried it out, and the effective rate reached 90%.

If you buy a car, you need to increase the price by 7% if you pay by installment. If you buy it in cash, you can deliver it at a 5% discount. Uncle Zhang calculated and found that the installment payment was 7200 yuan more than the cash purchase. The original price of this car is () yuan.

6. A new anti-influenza drug has been clinically tested in two hospitals in a city. It can be seen from the experiment that the effective rate of this medicine is ()%.

7. The cost of a commodity is 200 yuan, and the pricing profit is 30%. When you sell it, you will get a 10% discount, and there will still be a profit of ()%.

8. A batch of parts is completed in two days on average. The qualified rate of parts on the first day is 90%, and the qualified rate of parts on the second day is 95%. In two days, * * * produced 370 qualified parts, in two days, * * * produced () parts.

Second, the application problem

1. I was shocked to learn that after the tsunami in the Indian Ocean, teachers and students of our school donated money enthusiastically. In six years, the donations from girls in one class accounted for more than 40% of the class, and the donations from boys were the same as those from girls. How much did this class donate to the disaster area? (3 points)

2. 1999 1 month, Zhang Laohan deposited 8,000 yuan in the bank for 8 years, with an annual interest rate of 4.2%. However, in 2005 1 month, Zhang Laohan's wife was unfortunately ill and needed this 8,000 yuan urgently as medical expenses. According to bank regulations, time deposits are withdrawn in advance, and interest is calculated at the current interest rate of 1% per year. If he doesn't withdraw his deposit, Zhang Laohan can also borrow 8,000 yuan from the bank, and pay it off in one lump sum after maturity, but the annual interest rate is as high as 6%. From an economic point of view, you can calculate for Zhang Laohan by calculation. Which is more cost-effective to take out and borrow money in advance? (Interest tax is not considered in this question) (3 points)

3, a shopping mall during the Spring Festival to carry out preferential activities, provisions:

(1) If a shopping trip does not exceed 200 yuan, there will be no discount;

(2) If the purchase amount exceeds that of 200 yuan, but not more than that of 500 yuan (including 500 yuan), it will be sold at 10% off the list price, that is, at 10% off the list price;

(3) If the shopping exceeds that of 500 yuan at one time, 500 yuan will be given a discount according to Article (2), and the part exceeding 500 yuan will be given a 20% discount.