Integer equation - examples
- Real estate
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.
Cherries in the bowl can be divided equally among 11 or 16 or 4 children. How many is the minimum cherries in the bowl?
- Diofant 2
Is equation ? solvable on the set of integers Z?
Seedcake costs 50 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
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
How many times a day hands on a clock overlap?
- 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 c
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
- 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.
- 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
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.
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.
- 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)
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?
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.
- 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?
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.
- 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 an
- 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).
The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three?