# System of equations - examples - page 11

1. Holidays
Of the 35 students of class were 7 on holiday in Germany and just as much in Italy. 5 students visited Austria. In none of these countries was 21 students, all three visited by one student . In Italy and Austria were 2 students and in Austria and Germany.
2. 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.
3. Children
Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh?
4. 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
5. 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?
6. 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?
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. RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
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. 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?
11. 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.
12. 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?
13. 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?
14. 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?
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. Crown coins
Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
17. Two numbers
Find two numbers whose difference and ratio is 2.
18. Passenger car and truck
From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck?
19. The farmer
The farmer harvested 840 tons of grain in 2006, which was 44% less than in 2005, and one-fifth more than in 2004. How many tons of grain harvested in years 2005 and 2004?
20. Two pipes
One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?

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