# Examples for 8th grade

1. The price
The price of the land increased by 17%. What was the original price of the land if it now costs 46800 €?
2. Construct
Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
3. Subsets
How many 19 element's subsets can be made from the 26 element set?
4. Meat loses
Meat loses 18% of its weight by smoking. How much raw meat butcher used to manufacture 35 kilos of smoked?
5. Five pumps
The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps?
6. Trapezoid - intersection of diagonals
In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
7. Fractions
Three-quarters of an unknown number are 4/5. What is 5/6 of this unknown number?
8. Twelve
Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each one students did in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by express
9. Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
10. Bulb
A 60 W bulb consumes 0.12 kWh of electricity. How long did she stand light without a break?
11. Turners
Two turners perform joint work in 3 hours. The first turner would perform the job himself in 7 hours. How long would the same job last for a second turner if he worked alone?
12. Rectangle area
The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
13. Cinema tickets
Cinema sold 180 tickets this Thursday, which is 20%. Monday 14%, Tuesday 6%, Wednesday 9%, Friday 24%, Saturday 12%, and Sunday 15%. How many tickets were sold per week?
14. Water tank
A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
15. Mixture 2
How many liters of water must be added to 7 liters of a 20% solution to obtain a 10% solution?
16. The train
The train passed the observer in the 20s and passed through a 1500m tunnel in 2 minutes. Calculate the speed (km/h) and train length.
17. The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
18. Profit per kilo
The trader sells apples at a profit of 20% per kilogram. Today, he decided to reduce the price of apples by 10%. How much profit does the trader have today?
19. ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
20. Body diagonal
Calculate the length of the body diagonal of the 6cm cube.

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