Integer equation - examples
How many times a day hands on a clock overlap?
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
Cherries in the bowl can be divided equally among 11 or 16 or 4 children. How many is the minimum cherries in the bowl?
- Salary raise
Monthly salary was 2167 Eur. During the year it was raised to 2364 Eur. Calculate the month from salary was increased that employee earned 27186 Eur during whole year.
- Diofant 2
Is equation ? solvable on the set of integers Z?
- Diofant equation
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)
Seedcake costs 50 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
- 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 i
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
Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2.
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.
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.
The package has no more than 47 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 4.2 m of cloth and on one dress 1.1 m. Determine the amount of the cloth in the package.
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.
- Mushrooms from the forest
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?
- Digits A, B, C
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).
- Nice prism
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.
Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes?