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 third line has a written cube of a certain natural number.

Determine the smallest number Kate can think in the beginning.

Correct result:

n =  11250

Solution:

$$\begin{gathered} 9999<n<100000 \\ n=11250 \\ {l}_1=n+n\mathrm{/}2=11250+11250\mathrm{/}2=16875 \\ {l}_2=n+n\mathrm{/}5=11250+11250\mathrm{/}5=13500 \\ {l}_3=n+n\mathrm{/}9=11250+11250\mathrm{/}9=12500 \\ {l}_4=l_1+l_2+l_3=16875+13500+12500=42875 \\ {l}_5=35^3=42875 \\ n=11250 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• PIN code
  PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second d
• 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
• 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
• Self-counting machine
  The self-counting machine works exactly like a calculator. The innkeeper wanted to add several three-digit natural numbers on his own. On the first attempt, he got the result in 2224. To check, he added these numbers again and he got 2198. Therefore, he a
• Sugar - cuboid
  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
• Sales of products
  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?
• Two friends
  Two friends met as a good man perish together for a beer. After recovery the most important topics (politics, women, football ...), one asks: - And how many do you have children? - I have 3 children. - And how many years have? Friend already not want to a
• Endless lego set
  The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
• Divisibility
  Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero)
• 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
• Candy and boxes
  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
• Four-digit numbers
  Find four-digit numbers where all the digits are different. For numbers, the sum of the third and fourth digits is twice the sum of the first two digits, and the sum of the first and fourth digits is equal to the sum of the second and third digits. The di
• Chickens and rabbits
  In the yard were chickens and rabbits. Together they had 27 heads and 86 legs. How many chickens and how many rabbits were in the yard?
• Sum of three numbers
  The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
• 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.
• Cups
  We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then we
• Package
  The package has no more than 66 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 1.3 m of cloth and on one dress 5 m. Determine the amount of the cloth in the package.