# Examples for 9th grade - page 48

1. Ring The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
2. Seamstress Seamstress bought two kinds of textile together 25 meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?
3. 12 Moons Good Marry came to ask twelve moons for help with collecting strawberries. All twelve moons 1200 strawberries picked in 20 minutes. But lazy months July and August cease tear after 5 minutes. How many minutes in total will take collect strawberries?
4. Smallest internal angle Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
5. Solution What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
6. Line segment For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7 the distance from L to M.
7. Alfa, beta, gama In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
8. Count of triangles Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
9. Crowns 1180 crowns is divided into three people that A got 20% less than B and C by 15% more than B. How many got A,B and C?
10. Chocholate pyramid How many chocolates are in the third shelf when at the 8th shelf are 41 chocolates in any other shelf is 7 chocolates more the previous shelf.
11. Freight train The train carries 525 tons of limestone in 29 wagons. Wagons are 15 tonne and 20 tons. How many is 15 ton and how many is 20 ton wagons?
12. Jane and Miro Jane brother Miro is 42 years. And he is three times old as it was Jane when Miro was for so many years as there are now Jane. How old is Jane?
13. Three siblings Three siblings have birthday in one day-today. Together they have 35 years today. The youngest is three years younger than middle and the oldest is 5 years older than middle. How old is each?
14. Sprinter Sprinter runs the relay 4 x 400 m to the handover at speed 42 km/h. A second runner is at the start of the handover area 20 m long and runs when it is the first sprinter at distance 10 m. Calculate the speed at which the second runner must run in order to.
15. Rectangle - sides 3 If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we incr
16. Sportsman A trained athlete is able to exhale after a deep breath still 500 ml of air. At normal inhalation and exhalation is breathing 500 ml of air. Within one minute, one breath and exhaled 14 times. What part of breathing air per day is one exhalation?
17. Surface and volume od cuboid Content area of the square base of cuboid is Sp = 36 cm2 and its height 80 mm. Determine its surface area and volume.
18. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
19. Cube from sphere What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
20. Fifth of the number The fifth of the number is by 24 less than that number. What is the number?

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