Integer equation - problems

  1. MO Z8-I-1 2018
    age_6 Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
  2. Age
    age_5 In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
  3. Clock
    hodiny How many times a day hands on a clock overlap?
  4. 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
  5. Cherries
    visne Cherries in the bowl can be divided equally among 8 or 10 or 11 children. How many is the minimum cherries in the bowl?
  6. Salary raise
    euro Monthly salary was 2390 Eur. During the year it was raised to 2617 Eur. Calculate the month from salary was increased that employee earned 29361 Eur during whole year.
  7. Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  8. Seedcake
    pletenky Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
  9. 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)
  10. 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
  11. 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
  12. Divisibility
    dots Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. Package
    latky_textil The package has no more than 67 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 3.8 m of cloth and on one dress 1.7 m. Determine the amount of the cloth in the package.
  18. 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?
  19. 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).
  20. Daughters
    family_3 The man conducting the census asks a woman to age of three daughters. Woman says when multiply the age getnumber 72; if their ages add up, get a number of our house, as you see. The man says: That is not enough to calculate their ages. She says: my oldes

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