# Reason - problems

1. Pupils
There are 27 pupils in the classroom. They can swim 21 and ski nine pupils. Neither swim nor ski three pupils. How many pupils can swim and ski?
2. Dog price
Tereza agreed to get a dog and 6000 crowns a year for help in a dachshund breeding station. After eight months she had to finish work and got a dog and 2000 crowns. What price does a dog have?
3. Probability of intersection
Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?
4. Friction coefficient
What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
5. Iron pole
The iron pole is in the ground 2/5 of its length, partly above the ground 1/3 is yellow, and the unpainted section is 6 m long. How long is the entire column?
6. Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
7. A jackpot
How many times must I play this jackpot to win? A jackpot of seven games having (1 X 2), i. E. , home win or away win.
8. Barter
There is exchange trade on the market. We know that for two sheepskins we get three goat skins. We also know that for six rabbits skins we get four goat skins. How many rabbit's skins we get for four sheepskins?
9. Uphill and downhill
The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?
10. Last page
Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
11. Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
12. Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit
13. The work
The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take?
14. The King
The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?
15. Luggage and air travel
Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lugg
16. Brick weight
The brick weighs 2 kg and a half bricks. How much does one brick weigh?
17. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
18. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
19. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
20. Forestry workers
In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da

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