Examples for 8th grade - page 52

Fewer than 500 sheep,
There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?
Complementary angles
Two angles are complementary. If one angle measures 10°, what is the measure of the second angle?
Eva
When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet?
Interest p.a.
Calculate the value of interest in period of 1 year from the deposit 62000 CZK at 8 percent interest rate, after deducting 15 percent tax.
Two months
Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
Percent
From 99 children who participated in the ski course were 23 excellent skiers, 13 good and 20 average and the rest were beginners. Calculate this data in percentages.
Arithmetic average
The arithmetic mean of the five numbers is exactly 8. The sum of these four numbers is 30. What is the fifth number?
MATES
In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
Extreme temperatures
USA hit extreme heat wave. Calculate percentage of the air temperature change from normal summer temperature 23 °C to 40 °C.
Arc-sector
arc length = 17 cm area of sector = 55 cm² arc angle = ? the radius of the sector = ?
The field
The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
Travel by bus
Five girls traveling by bus. Each holds in each hand two baskets. Each basket contains 5 cats. Each cat has 5 kittens. 3 girls getting off the bus and another girl without baskets go on board. The bus control driver. How many legs are in the bus?
Rectangular field
One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m² . Determine dimencions of the field.
Square circles
Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
Obtuse angle
The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
Pool
Pool is filled with two water supply. The first supply fill pool for nine hours, the second for six hours. How many hours will take fill the pool when the water flows in through the first supply 3 hours and then we will open a second supply?
Isosceles trapezoid
What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
Laths
There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide

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