Integer equation - examples

  1. Clock
    hodiny How many times a day hands on a clock overlap?
  2. Z9-I-4
    numbers_30 Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
  3. Cherries
    visne Cherries in the bowl can be divided equally among 11 or 16 or 4 children. How many is the minimum cherries in the bowl?
  4. Salary raise
    euro Monthly salary was 2167 Eur. During the year it was raised to 2364 Eur. Calculate the month from salary was increased that employee earned 27186 Eur during whole year.
  5. Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  6. Diofant equation
    diofantos In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
  7. Seedcake
    pletenky Seedcake costs 50 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
  8. Sugar - cuboid
    kocky_cukor Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i
  9. Group
    deti_skupina Group of kids wanted to ride. When the children were divided into groups of 3 children 1 remain. When divided into groups of 4 children 1 remain. When divided into groups of 6 children 1 missed. After divided to groups of 5 children its OK. How many are t
  10. Divisibility
    dots Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2.
  11. Rectangle
    rectangles_1 The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
  12. Line
    negative_slope Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
  13. Package
    latky_textil The package has no more than 47 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left remain. On the one blouse consumes 4.2 m of cloth and on one dress 1.1 m. Determine the amount of the cloth in the package.
  14. Basements
    Spider-and-Fly In the first basement is more flies than the spiders, the second vice versa. Each basement had spiders and flies together 100 feet. Determine how many could be flies and spiders in the first and second basement. PS. We only need, when you write how many.
  15. Mushrooms from the forest
    dubak Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda?
  16. Digits A, B, C
    numbers_8 For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product).
  17. Nice prism
    diagonal_rectangular_prism.JPG Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
  18. Friends
    friends2 Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
  19. Legs
    zidle In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
  20. Cooks
    kucharky Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes?

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