# High school + system of equations - examples

1. Potatoes
For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
2. Nine books
Nine books are to be bought by a student. Art books cost \$6.00 each and biology books cost \$6.50 each . If the total amount spent was \$56.00, how many of each book was bought?
3. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
4. 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.
5. 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.
6. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
7. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
8. Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
9. Rectangle - sides ratio
Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
10. Gear
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
11. R triangle
Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
12. Pedestrian up-down hill
Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
13. Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
14. The cyclist
The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town.
15. Tourists
From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?
16. Ships
At 8:40 the ship set sail at 12 km/h. At 19:10 followed by at 29 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took?
17. Team
The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player?
18. Freedom
In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
19. Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump?
20. Trains
From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains.

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