# Algebra - problems - page 3

1. TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
2. Beer
After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
3. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
4. Root
The root of the equation ? is: ?
5. Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth l
6. Coffee
In stock are three kinds of branded coffee prices: I. kind......248 Kč/kg II. kind......134 Kč/kg III. kind.....270 Kč/kg Mixing these three species in the ratio 10:7:7 create a mixture. What will be the price of 1100 grams of this mixture?
7. Motion
If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure. How far is the train station?
8. Store
One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
9. Hands
The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
10. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
11. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
12. Clock
How many times a day hands on a clock overlap?
13. Server
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
14. Chickens and rabbits
In the yard were chickens and rabbits. They had 28 heads and 82 legs. How many chickens and how many rabbits was in the yard?
15. Z9-I-4
Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
16. Bus vs. train
Bus started from point A 10 minutes before the train started from the same place. The bus went an average speed of 49 km/h, train 77 km/h. To point B train and bus arrived simultaneously. Calculate time of train journey, if train and bus travelled the.
17. Inflation
What is better for people (employees)? ?
18. Discount
Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 70 USD. Determine the original price of sweater.
19. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
20. Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?

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