System of equations + reason - math problems

  1. Three parallels
    rs_triangle The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
  2. Glasses
    okuliare There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls?
  3. The escalator
    eskalator I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I climb
  4. Two math problems
    coins 1) The sum of twice a number and -6 is nine more than the opposite of that number. Find the number. 2) A collection of 27 coins, all nickels, and dimes, is worth $2.10. How many of each coin are there? The dime, in United States usage, is a ten-cent coin
  5. Circus
    cirkus On the circus performance was 150 people. Men were 10 less than women and children 50 more than adults. How many children were in the circus?
  6. The devils
    cert The devils weighed in hell with Dorota. They found that Dorota and the two devils weigh 250 kg together and Dorota and the four devils weigh 426 kg. All the devils weigh the same. How Much Does Dorota Weigh?
  7. Students
    skola After the fifth-grade class left 20% of students. In the seventh grade were added 2 pupils, in the eighth 1 pupil, in the ninth, the number has not changed, but it is now tenth students less than it was in the fifth grade. How many pupils are in the 9th.
  8. Long bridge
    bridge Roman walked on the bridge. When he heard the whistle, he turned and saw running Kamil at the beginning of the bridge. If he went to him, they would meet in the middle of the bridge. Roman, however, rushed and so did not want to waste time returning 150m..
  9. Two cities
    cars_30 The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
  10. Dividing money
    mince_2 Vilem, Cenek, and Edita divided the money they earned by spreading the leaflet. Vilem got 240 CZK more than Cenek and twice more than Edita. Edita got 400kc less than Vilem.
  11. Flowerbed
    circles We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
  12. Time passing
    clock-night-schr 6 years ago, Marcela's mother was two times older than her and two times younger than her father. When Marcela is 36, she will be twice as young as her father. How old are Marcela, her father, and mother now?
  13. Dog price
    dog Tereza agreed to get a dog and 6000 crowns a year for help in a dachshund breeding station. After eight months she had to finish work and got a dog and 2000 crowns. What price does a dog have?
  14. Rectangles
    rectangle_15 The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
  15. Unknown numbers
    eq222_3 The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
  16. Supermarket 2
    pie_3 A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution.
  17. Four numbers
    equilateral_triangle_5 The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
  18. Square into three rectangles
    stvorcove-cisla_1 Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
  19. Beds
    stan_3 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?
  20. Candy and boxes
    cukriky_13 We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of.

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