# Examples for 9th grade - page 70

1. Three figures - numbers
The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures.
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?
3. 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.
4. 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
5. Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
6. 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.
7. 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.
8. 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?
9. 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?
10. Resistance
Determine the resistance of the bulb with current 200 mA and is in regular lamp (230V).
11. 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.
12. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
13. 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.
14. Isosceles trapezoid
Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
15. 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?
16. Two numbers
The sum of the two numbers is 1. Find both numbers if you know that half of the first is equal to one seventh of the second number.
17. Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
18. Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
19. Brick wall
Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. Wall will be built on the garden ground. How many will we need bricks if to 1 m³ is required approximately 300 bricks?
20. Rabbits 3
Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?

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