Z9-I-4

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. Finally, all three lines sum and result wrote on the fourth line. Then she was amazing found that on the fourth line has writed cube of certain natural number.

Determine the smallest number Kate can think in the beginning.

Result

n =  11250

Solution:

Solution in text n =







Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

Next similar examples:

  1. Digit sum
    number_line_3 The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
  2. Real estate
    house Residential house has three entrances numbered by odd numbers arithmetic progression. The sum of the two numbers on the corner entrances is 50. Calculate the highest of this three numbers.
  3. Sales of products
    cukriky_9 For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
  4. 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.
  5. Segments
    segments Line segments 67 cm and 3.1 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
  6. Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  7. 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)
  8. 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?
  9. Seedcake
    pletenky Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
  10. Four integers
    tiles2 Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
  11. Blades
    ruler2_1 1st blade 2,5 m, 2nd blade. .1.75 m. How many same long pieces of this two blades can be do the biggest? How long is one piece?
  12. Three friends
    gulky_9 Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
  13. Paving - joints
    tiles_6 We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and in the second row in width etc. How many times will the joints meet at a distance 10 m?
  14. Odd numbers
    friends4_2 The sum of four consecutive odd numbers is 1048. Find those numbers ...
  15. Cuboid walls
    cuboid_9 Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
  16. Dining tables
    stolik In the dining room are tables with 4 chairs, 6 chairs, 8 chairs. How many diners must be at least to be occupy all tables (chairs) and diners are more than 50?
  17. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.