Fractions + Mathematical Olympiad - practice problems
Number of problems found: 13
- Sufficiently 7059
The king gave the mason Václav the task of building a wall 25 cm thick, 50 m long, and 2 m high. If Václav had worked without a break and at the same pace, he would have built a wall in 26 hours. However, according to the valid royal regulations, Wencesla - Centipede 4257
Centipede Mirka consists of a head and several articles. Each pair has one pair of legs. When it got cold, she decided to get dressed. Therefore, she put on a sock on her left foot in the third article from the end and then on every other third article. S - Shepherd
Kuba makes a deal with a shepherd to take care of his sheep. Shepherd said to Kuba that he would receive twenty gold coins and one sheep after a year of service. But Kuba resigned just after the seventh month of service. But the shepherd rewarded him and - Manufacturer 6981
The hotelier wanted to equip the dining room with new chairs. He chose the type of chair in the catalog. Only when placing an order did he learn from the manufacturer that they offered every fourth chair at half price as part of the discount offer and tha - Celebration 4461
Anička has 50 CZK, Anežka has 46 CZK, and they want to use all the money to buy desserts for a family celebration. They decide between cakes and pinwheels. A pinwheel is CZK 4 more expensive than a cake, and for all the money, you could buy a third more c - Originally 5427
There were red and green candies in the tin. Čenek ate 2/5 of all the red candies, and Zuzka ate 3/5 of all the green candies. Now, the red candies make up 3/8 of all the candies in the can. How many candies were originally in the can? - Soup
On Monday, we cook 25 pots and ten boilers of soup. On Tuesday, 15 pots and 13 boilers. On Wednesday, 20 pots and on Thursday, 30 boilers. On Monday and Tuesday was cooked the same amount of soup was. How many times is more soup cooked on Thursday than on - Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - Meadow
On the meadow grazing horses, cows, and sheep, together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equal. How many horses, cows, and sheep are on the meadow togethe - Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Quadrilaterals 7224
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M and divide the dode - Perpendicular 7223
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M. The quadrilateral - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl
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