# Examples for 9th grade - page 67

1. Sweets We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
2. Rectangle - sides 4 Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
3. Unknown number 10 Number first increased by 30%, then by 1/5. What percentage we've increased the original number?
4. Steamer At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer?
5. Pet store In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more th
6. Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
7. Hydrochloric acid Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?
8. Three ints The sum of three consecutive integers is 2016. What numbers are they?
9. Skiing meeting On the skiing meeting came four friends from 4 world directions and led the next interview. Charles: "I did not come from the north or from the south." Mojmir "But I came from the south." Joseph: "I came from the north." Zdeno: "I come from the south." W
10. Circular lawn Around a circular lawn area is 2 m wide sidewalk. The outer edge of the sidewalk is curb whose width is 2 m. Curbstone and the inner side of the sidewalk together form a concentric circles. Calculate the area of the circular lawn and the result round to 1
11. Prism - eq triangle Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
12. Eight palm There grows 8 palms by the sea. At the first sitting one parrot, on second two, on third sits four parrots on each other twice the previous parrots sitting on a previous palm. How many parrots sitting on eighth palm?
13. Octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
14. Roof tiles The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m2 should be used 8 tiles?
15. Forces Determine the resultant of two perpendicular forces F1 = 560 N and second force of 25% smaller.
16. PIN - codes How many five-digit PIN - code can we create using the even numbers?
17. Umbrella Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm.
18. Seamstress 2 Seamstress bought two kinds of textile in whole 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?
19. Dollars Mama split 760 dollars Jane, Dane and Eva as follows: Jane got three times more than Dane and Dane and got 40 more than Eva. How much does get each of them?
20. Circumscribed circle to square Find the length of a circle circumscribing a square of side 10 cm. Compare it to the perimeter of this square.

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...