# 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:

$9999 < n < 100000 \ \\ n = 11250 \ \\ l_{ 1 } = n+n/2 = 11250+11250/2 = 16875 \ \\ l_{ 2 } = n+n/5 = 11250+11250/5 = 13500 \ \\ l_{ 3 } = n+n/9 = 11250+11250/9 = 12500 \ \\ l_{ 4 } = l_{ 1 }+l_{ 2 }+l_{ 3 } = 16875+13500+12500 = 42875 \ \\ l_{ 5 } = 35^3 = 42875 \ \\ n = 11250$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! Tips to related online calculators
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

## Next similar math problems:

1. Digit sum How many are three-digit numbers that have a digit sum of 6?
2. Girls The boys and girls in the class formed without the rest of the fives, 2 girls and 3 boys. There are 6 girls missing to create mixed pairs (1 boy and 1 girl). How many girls are in the classroom?
3. Age In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
4. Solve 2 Solve integer equation: a +b+c =30 a, b, c = can be odd natural number from this set (1,3,5,7,9,11,13,15)
5. Average monthly salary A total of 10 teachers work at one small school in Moravia. The monthly salary of each is 21,500 CZK or 21,800 CZK or 22,500 CZK according to their education and age. The average monthly salary for this school's teacher is 21 850 CZK. How many teachers of
6. 600 pencils 600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
7. MO Z8-I-1 2018 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.
8. The Hotel The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r
9. Rectangles How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.
10. Red and white Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the optio
11. Apples and pears Apples cost 50 cents piece, pears 60 cents piece, bananas cheaper than pears. Grandma bought 5 pieces of fruit, there was only one banana and paid 2 euros 75 cents. How many apples and how many pears?
12. Chocolate I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate.
13. Year 2018 The product of the three positive numbers is 2018. What are the numbers?
14. Diofant equation 250x + 120y = 5640
15. Math test In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?
16. Rectangles Vladimir likes to draw rectangles. Yesterday he created all rectangles that had sides in centimeters and a circumference of 18 cm. How many rectangles of different dimensions have been drawn?
17. Two integers Two integers, a and b, have a product of 36. What is the least possible sum of a and b?