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:

$9999 < n < 100000 \ \\ n=11250 \ \\ l_{1}=n+n/2=11250+11250/2=16875 \ \\ l_{2}=n+n/5=11250+11250/5=13500 \ \\ l_{3}=n+n/9=11250+11250/9=12500 \ \\ l_{4}=l_{1}+l_{2}+l_{3}=16875+13500+12500=42875 \ \\ l_{5}=35^3=42875 \ \\ n=11250$

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. One hundred stamps
   A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths , one crown, two-crown and five-crown. How many are each type of stamps? How many does the problem have solutions?
2. Last digit
   What is the last number of 2016 power of 2017
3. Three-digit
   How many three-digit natural numbers do not have the number 7?
4. Six-digit primes
   Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
5. 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 opti
6. 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?
7. Remainder
   A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
8. Cakes Z8-I-5
   Mom brought 10 cakes of three types: kokosek was less than laskonek and most were caramel cubes. John chose two different kinds of cakes, Stephan did the same and for Margerith leave only the cakes of the same type. How many kokosek, laskonek and caramel
9. Intelligence test
   Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions. After the test, K
10. Unknown number
    Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The prod
11. Tunnels
    Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to an
12. Skiing meeting
    On the skiing meeting came four friends from 4 world directions and led the next interview. Charles: "I did not come from the north or from the south." Mojmir "But I came from the south." Joseph: "I came from the north." Zdeno: "I come from the south."
13. Divisors
    The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
14. Toy cars
    Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
15. Z9–I–4 MO 2017
    Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conduct
16. Cube root
    Find cube root of 18
17. Pet store
    In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more t