# Examples for 9th grade - page 64

1. Right triangles How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
2. Locomotive Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done?
3. Tonic One package tonic consume Mom 12 weeks and daughter for 14 weeks. 4 weeks they use the same cream together and then only daughter. How many weeks endured tonic to daughter then?
4. Painting The room is long 50 meters and wide 60dm and 300 cm high. Calculate how much it will cost painting if area of windows and doors is 15% of the total area. One square meter cost 50cents.
5. Concentration How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%? Product of two numbers is 900. If we increase lowest number by 2 then product will increase by 150. Determine both numbers.
7. Three friends The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid? What is the slope of a ladder 6.2 m long and 5.12 m in height.
9. Dried apples How many kilograms of fresh apples id needed to 120 kg of dried apples when from 0.4 tons of fresh apples we get 75 kg of dried apples?
10. Real estate Residential house has three entrances numbered by odd numbers arithmetic progression. The sum of the two numbers on the corner entrances is 50. Calculate the highest of this three numbers.
11. Digging A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ?
12. Water channel The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow
13. Quatrefoil Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
14. Piano If Suzan practicing 10 minutes at Monday; every other day she wants to practice 2 times as much as the previous day, how many hours and minutes will have to practice on Friday?
15. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
16. Four swords Obelix has three helmets, four swords and five shields. How many swords must make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor? Determine the number of integers from 1 to 106 with ending four digits 2006.
18. Freezer The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, 30 cm. A layer of ice of 23 mm thick was formed on the inner walls (and on the opening) of the freezer. How many liters of water will drain if we dispose the freezer?
19. Enrollment The enrollment at a local college increased 4% over last year's enrollment of 8548. Find the increase in enrollment (x1) and the current enrollment (x2).
20. Gasoline 35 l of gasoline is to be divided into four canisters so that in the third canister was 5 l less than the first canister, the fourth canister 10 l more than in the third canister and the second canister half what in the first canister. How many liters of.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...