# Examples for 9th grade - page 71

1. Theatro
Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?
2. Cycling trip
At 8 am started a group of children from the camp to day cycling trip. After 9:00 weather deteriorated sharply and the leader decided to send for the children bus on the same route, which started at 10 hours. For how long and at what distance from the camp
3. Digits
How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated.
4. Potatoes
Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself.
Number 118 divide into two addends, so first addend is 69 greater than 75% of the second addend.
6. Contestants
In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestan
If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?
8. Three figures - numbers
The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures.
9. Hexagonal prism 2
The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
10. Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
11. Candy
The price for 1kg of more expensive candy is 125 CZK. The price for 1kg of cheaper candy is 100 CZK. We make two different blends of candy. And now. The second blend contains 2kg of more expensive candy and several kg of cheaper candy. The price per 1 kg o
12. Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
13. Regular octagon
Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.
14. Centre of mass
The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
15. Diameters of circles
How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
16. Cruise liner
Cruise liner runs along the river between points A and B. The journey downstream takes 40 minutes 1 hour upriver. The flow rate of the river is 3 km/h. What is the speed of cruise liner?
17. Roses 2
Aunt Rose went to the flower shop to buy a bouquet with three roses. The flower shop had white, yellow and red roses. How many different flowers bouquet can a flower make for Aunt Rose create? Write all the bouquet options.
18. Family parcels
In father will he divided the land so that the older son had three bigger part than younger son. Later elder son gave 2.5 ha field to younger and they had both the same. Determine the area of family parcel.
19. Pyramid Z8–I–6
Each brick of pyramid contains one number. Whenever possible, the number in each brick is lowest common multiple of two numbers of bricks lying directly above it. That number may be in the lowest brick? Determine all possibilities.
20. Cost reduction
Two MP3 players whose price was equal to originally have been discounted the first by 20%, the second by 35%. After the price reduction was the difference in their prices 750, - CZK. What was the original price of each of the two players?

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