# Examples for 8th grade - page 107

1. Equation - inverse Solve for x: 7: x = 14: 1000
2. Summer tires Three tire servants have to change the summer tires on 6 cars in 2 hours. Mark's replacement would take 4.5 hours, Jirka would do it in 3 hours and 10 minutes, and Honza in 4 hours. Will they be able to replace all tires at the desired time?
3. Soup from canteen For how many people is 90 liters of soup enough if we assume 3/8 liter of soup per person in the canteen?
4. Cube into cylinder If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
5. Bottle A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
6. Marriage sttus In our city, there are 3/5 of the women married to 2/3 of the men. Find what part of the population is free.
7. Beds At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed?
8. Pool tiles The pool is 25m long, 10m wide and 160cm deep. How many m2 of tiles will be needed on the walls and the pool? How many pieces of tile are needed when 1 tile has a square shape with a 20cm side? How much does it cost when 1m2 of tiles costs 258 Kc?
9. Three segments The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
10. Hectares The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor
11. Clothes Danka and Janka collect clothes. Danka had 9 more than Janka, so she gave her 7. Which now has more cloth and how many?
12. 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?
13. Simple equations Solve system of equations: 5x+3y=5 5x+7y=25
14. Resistance A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
15. Perfect cubes Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube?
16. A truck A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
17. A residential A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the
18. The volume The volume of a solid cylinder is 260 cm3 the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
19. Practice How many ways can you place 20 pupils in a row when starting on practice?
20. The price The price of the land increased by 17%. What was the original price of the land if it now costs 46800 €?

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