Examples for 9th grade - page 97

2 pipes
2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone?
Honza
Honza is 13 years old and Peter 21 years old. After how many years are their ages will be at ratio 7: 9?
Two masters
The two masters will make as many parts as five apprentices at the same time. An eight-hour shift begins at 6 o'clock. When can a master finish the job to produce just as much as an apprentice for the whole shift?
Cube root
Find cube root of 18
Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
Bulb
A 60 W bulb consumes 0.12 kWh of electricity. How long did she stand light without a break?
Square sides
If the square side increases by 28%, the square circumference increases by 11.2 meters. Find the length of the original square side.
The larger
The larger of two numbers is nine more than four times the smaller number. The sum of the two numbers is fifty-nine. Find the two numbers.
Apples
Zuzana bought 3 kg Jonathan apples. Then she noticed that Golden apples were 3 CZK a kilogram cheaper. So they bought 2 kg. For apples, she paid a total of CZK 109. How much did 1 kg Jonathan and how much Golden?
Oranges
Mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there?
Age
In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
Special watch
Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?
Bottles
The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
The cube
The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
Scientific notation
Approximately 7.5x10⁵ gallons of water flow over a waterfall each second. There are 8.6x10⁴ seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day.
A boy
A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
Isosceles trapezoid
The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
A man 2
A man divides $10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.

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