# Examples for 8th grade - page 107

1. 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.
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. 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.
4. 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?
5. Volcano
The crater of a volcano is approximately in the shape of a cone of a base 3.1416 sq. Mi. The crater's depth is 1500 ft. How many cubic yards of earth would be required to fill this cavity?
6. 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?
7. 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?
8. 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?
9. Simple equations
Solve system of equations: 5x+3y=5 5x+7y=25
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. 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?
12. Sewing
Beth's mother can sew 235 pairs of short pants in 6 days while Lourdes can sew 187 pairs in 8 days. How many more pairs of short pants can Beth's mother sew?
13. 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)?
14. 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
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. The price
The price of the land increased by 17%. What was the original price of the land if it now costs 46800 €?
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. Ladder
Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
19. 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.
20. Cube walls
Find the volume and the surface area of the cube if the area of one of its walls is 40 cm2.

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