1. A ship departs from a port 240 nautical miles apart and reaches its destination 48 nautical miles ago, with its speed decreasing by nautical miles per hour. The total time taken after arrival is equal to the original speed MINUS the time spent on the whole voyage of 4 knots, and the original speed is found.
2. Last year, two workshops A and B of a factory planned to complete tax profits of 7.5 million yuan. As a result, workshop A exceeded the plan 15% and workshop B exceeded the plan%, and both workshops completed tax profits of 8.45 million yuan. How much tax and profit did these two workshops complete respectively last year?
3. It is known that the sum of the original prices of commodities A and B is 150 yuan. Due to market changes, the prices of A and B decreased by% and increased by 20% respectively. After the price adjustment, the sum of the unit prices of A and B decreased by 65,438+0% compared with the sum of the original unit prices. What are the original unit prices of A and B respectively?
Xiaohong bought two children's toothbrushes and three toothpastes in the shop last summer vacation, and just ran out of money with him. It is known that each toothpaste is more than each toothbrush 1 yuan. This summer, she bought the same toothbrush and toothpaste in the store with the same money, because each toothbrush rose to 1.68 yuan this year, and the price of each toothpaste increased by 30%. Xiaohong had to buy two toothbrushes and two toothpastes, and finally got back 40 cents. How much is each toothpaste?
5. If a shopping mall sells goods with a unit price of 8 yuan per piece 12 yuan, it can sell 400 pieces every day. According to experience, if each piece is sold less 1 yuan, you can sell more than 200 pieces every day. How much should each piece be reduced to get the best benefit?
2. Simple Seventh Grade Olympic Title II
1. It takes 5 days for A and 6 days for B to complete a job, or 7 days for A and 2 days for B. Q: How many days does it take for Party A and Party B to do this job alone?
2. There are three alloys: the first one contains 60% copper and 40% manganese; The second one contains manganese% and nickel 90%; The third alloy contains 20% copper, 50% manganese and 30% nickel. Now a new alloy containing 45% nickel is composed of these three alloys, and its weight is 1 kg.
(1) Try to express the weight of the second alloy by the weight of the first alloy in the new alloy;
(2) Find out the weight range of the second alloy in the new alloy;
(3) Find out the weight range of manganese in the new alloy.
3. Given 3x2-x= 1, find the value of 6x3+7x2-5x+2000.
4. A store sells 0 items a day, and each item can make a profit in 4 yuan. Now they increase profits by raising prices and reducing purchases. According to experience, every time the price of this commodity increases by 1 yuan, they sell fewer pieces every day. How much can each item be lifted to make a profit? What's the profit?
5. It is known that cb⊥ab, ce ∠bcd, de ∠cda, ∠ 1+∠ 2 = 90. Verification: da⊥ab.
3. Simple seventh-grade Olympic mathematics third question
1. Find the integer solution of the indefinite equation 49x-56y+ 14z=35.
2. Eight men and eight women dance in groups.
(1) If there are two substations, male and female;
(2) If men and women stand in two rows, in no particular order, only consider how men and women form partners. How many different situations are there?
3. How many of the five numbers1,2, 3, 4 and 5 are greater than 34 152?
4.A train is 92 meters long and B train is 84 meters long. If they travel in opposite directions, they will miss each other after 1.5 seconds. If they travel in the same direction and miss each other after 6 seconds, find the speed of the two trains.
Two production teams of Party A and Party B grow the same vegetables, and after four days, the rest will be finished by one team of X, which will take another two days. If Party A finishes all the tasks by itself three days faster than Party B, how many days does it take to ask Party A to finish it by itself?
4. Simple seventh-grade Olympic fourth question
1. Find the integer solution of equation | xy |-| 2x |+y | = 4.
2. Wang Ping bought a 3-year Treasury bill with an annual interest rate of 7. % and the annual interest rate is 7.86% * * 35,000 yuan. If the three-year Treasury bonds expire, the principal and interest will be deposited in two consecutive one-year time deposits. After five years, the total principal and interest of the five-year Treasury bonds will be 477,665,438+0 yuan. How much will Wang Ping spend on three-year national debt and five-year national debt? (It is known that the annual interest rate of one-year time deposit is 5.22%)
3. Find the integer solution of the indefinite equation 3x+4y+ 13z=57.
Xiao Wang bought 40 fruits with 5 yuan money to entertain five friends. There are three kinds of fruits: apples, pears and apricots, each with 20 points, 8 points and 3 points respectively. Xiao Wang hopes that he and his five friends can get apples. Everyone gets a different number of apples. Can he achieve his wish?
5. Find the sum of the coefficients in the expansion of (8x3-6x2+4x-7)3(2x5-3)2.
5. Simple seventh-grade Olympic fifth question
1. It takes 30 days for Party A to draft and 20 days for Party B to draft alone. After playing together for a few days, Party A stopped to have a rest, and Party B continued to play for five days. How many days did a play last?
2. build a road, team a can finish it in 20 days, and team b can finish it in 25 days. Now the two teams are repairing together, team A has three days off and team B has a few days off, so it took 15 days to finish the repair. How many days did Team B rest?
3. It takes 65,438+02 days for Party A to transport a truck, 65,438+05 days for Party B and 20 days for Party C.. There are the same loading M and N, with A loading M and B loading N at the same time. C began to help A move, helped B move halfway, and finally moved two cars at the same time. How many hours did C help A?
4. If you finish a job alone, it takes 10 days for Xiao Zhang, 12 days for Xiao Li and 15 days for Xiao Wang. Now the three of them work together. Xiao Zhang rested 1 day in the middle, Xiao Li rested for 3 days, and Xiao Wang worked until the completion. How many days did it take?
Party A and Party B work together to complete a project within 20 days. If Team A works for 7 days and Team B works for 5 days, only 1/3 can be completed. How many days does it take for each team to complete the task alone?
6. Party A works alone for 3 days, and then works with Party B for 5 days, thus completing half of the whole project. It is known that the ratio of working efficiency of A and B is 3: 4. If b does it alone, how many days will it take to finish?