# Examples for 7th grade (seventh) - page 35

1. Angles of a triangle In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
2. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
3. Car consumption The car has consumption 4 l/100 km. How much money will it cost ride 4 km in long if diesel price is 1.53 USD/l?
4. Is right triangle One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
5. Children Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh?
6. Cube 3 How many times will increase the volume of a cube if we double the length of its edge?
7. Prism Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
8. 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?
9. 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?
10. Smallest internal angle Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
11. The balls You have 108 red and 180 green balls. You have to be grouped into the bags so that the ratio of red to green in each bag was the same. What smallest number of balls may be in one bag?
12. Janitor Janitor tosses 26 cm layer of snow on the school grounds for 90 minutes. How many friends would have to call for help if snow needs to have bowled for 15 minutes. We assume that at the same time bow all the same amount of snow.
13. Feed for horses In the kennel have feed for two horses for 21 days. The station brought an additional 5 horses. How many days will last the feed for all the horses if they have the same daily ration? The size of two internal angles of a triangle ABC are α=6/18π and β=7/18π. Calculate the size of the third angle.
15. Hockey teams goals Hockey teams fired 200 goals. The second team 13 less than first team, third 16 less than the first and fourth tean 19 goals less than first. How many goals fired each team?
16. Ratio v2 Decrease in the ratio 12:16 number 13.2.
17. 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?
18. 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?
19. 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.
20. Pavilion The rectangular pavilion with dimensions 3.5 m and 2.75 m to be paved with square tiles of side 25 cm price of CZK 22 per 1 piece or rectangular tiles with sides of 20 cm and 15 cm in the price of CZK 11 per 1 pc. Which solution is cheaper (write its price

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