# Reason - examples - page 32

1. 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.
2. Three machines The power of the three machines is 2: 3: 5. Two most powerful machines produce 400 parts per hour. How many components make all three machines in 3 hours?
3. A clock A clock was set right at 6:00 AM. If it gains 3 1/2 minutes per hour, what time will it show at 6:00 PM on the same day? Show your solution
4. Two rectangles I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calcu
5. Supermarket 2 A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution.
6. Page numbering The book has 88 pages. How many times is the number 4 used for the book numbering?
7. Two trains Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak
8. Saving 9 An amount if \$ 2000 is invested at an interest of 5% per month. if \$ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount have accumula
9. Father and sons After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now?
10. Test The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers.
11. School Less than 500 pupils attend school. When it is sorted into pairs, one pupil remains. Similarly, when sorted into 3, 4, 5 and 6 members team one remains. Sorted to seven members teams, no left behind. How many pupils are attending this school?
12. The coil How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
13. Triangles Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have?
14. Left handed It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
15. 7 digit number If 3c54d10 is divisible by 330, what is the sum of c and d?
16. MO C–I–1 2018 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
17. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
18. Rectangles The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
19. Snacks The school attends 344 pupils. Half of them take snacks. 13 pupils who took snacks did not attend school. How many snacks left?
20. Tractors 5 tractors will plow the field for 8 hours. In 2 hours, 1 tractor broke down. How long do the remaining tractors complete the plow?

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