# System of equations - examples - page 16

1. Sweets 3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations
2. Cork and swimming If a person weighs 80 kg, how many kilograms of cork must take swimming belt to use it to float on water? The density of the human body is 1050kg/m3 and cork 300kg/m3. (Instructions: Let the human body and cork on a mixture that has a density of 1000kg/m
3. Rectangle The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?
4. Cuboid - edges The sum of all edges cuboid are 8 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid.
5. Barbara Barborka goes to school with backpack that was 2 - times more expensive than a bag slipper. If backpack was 36 euros cheaper it was cost same as bag slipper. How many cost backpack and how many bas slipper?
6. Two numbers Determine the numbers x and y so x + y = 8 is truth and the numbers are in the ratio of 4: 5.
7. Unions now The plant has 1,250 employees. The Trade Unions (former ROH, OH) is 18% male, 23% female. Plant management reported that in the trade union is 20% of all employees. How many men and women are in plant and how many are men and women in trade unions?
8. Angle Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
9. Pages of book Lenka calculated that if every day to read 16 pages of the book, read a book a day earlier than had read only 14 pages a day. How many pages has this book?
10. Testing Students of high school have 10 points for each good solved task. The wrong answer is deducted by 5 points. After solving 20 tasks, student Michael had 80 points. How many tasks did he solve correctly and how many wrong?
11. Sebastian From Kovalov Sebastian walks at 6 km / h started at 8:00 in the direction of Kuty. From Kuty, the godfather is driving at 50 km/h and started at 8:30. The distance is 24 km. When and where grandfather will take Sebastian to the car.
12. Concentration How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%?
13. Three friends The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid?
14. Odd numbers The sum of four consecutive odd numbers is 1048. Find those numbers ...
15. Hostel Students are accommodated in 22 rooms. Rooms were 4 and 6 bed. How many rooms in which type occupied 106 children there?
16. Gasoline 35 l of gasoline is to be divided into four canisters so that in the third canister was 5 l less than the first canister, the fourth canister 10 l more than in the third canister and the second canister half what in the first canister. How many liters of.
17. Nuts Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts.
18. Three friends Divide 570 euros to three friends so that first will get 50 euros less than the second and third twice more than the first. How many euros will get everyone?
19. Football league In the 2nd football league plays each of the 16 participants with each opponent twice. For every victory gets 3 points, 1 point for a draw, a defeat none. After the competition was team with 54 points and 12 defeats at 9th place. How many times have won?
20. Numbers at ratio The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?

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