# System of equations - examples - page 25

1. Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
2. Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
3. Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
4. Gasoline tank 2
A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
5. Candy and boxes
We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of.
6. Speed of car
The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
7. Supermarket 2
A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution.
8. Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
9. Two cities
The distance between cities A and B is 132 km. At 9.00 am, the cyclist started the bike at an average speed of 24 km/h, and at 10.00 h started from the B cyclist at an average speed of 30 km/h. How long and far from A will they both meet?
10. Two trains
Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak
11. Father and sons
After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now?
12. The tourist
The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
13. Viju
viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with viju??
14. Inscribed circle
Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
15. Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
16. Flowerbed
Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
17. Rectangles
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
18. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
19. Parking
At a building parking, 245 spaces are for cars, 56 are for vans and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses?
20. Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.

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