# Reason - examples - page 30

1. 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 the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
2. Family 8
Father is 38 years old, daughter 12, son 14. How many years will father have as many years as his children together?
3. Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
4. Suzan
Susan's age will be after 12 years four times as much as twelve years ago. How old is Susan now?
5. Summands
Find two summands of the number 42, so that its product is minimized.
6. One hundred stamps
A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths , one crown, two-crown and five-crown. How many are each type of stamps? How many does the problem have solutions?
7. Warmer weather
This morning it was -6 °C. What temperature did the thermometer show yesterday if it was three times warmer?
8. House numbering
The residential house has three entrances numbered even numbers, successive immediately behind. The sum of the two numbers on the outside entrances is 68. Calculate the middle of these three numbers.
9. Train delay
The train should be in the station for 10 minutes. It still has 32 km left. What is the expected delay if the train travels in 2 minutes 3 km except for the last section where it is 2 km in 5 minutes.
10. Ľé sweets
There are 20 sweets in the bag. Some are chocolate, other coconuts, and the remaining marzipan. Chocolate is 4 times more than coconut. Marzipan's less than chocolate. How much is in a bag of coconut sweets?
11. Clouds
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
12. Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
13. Prove
Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
Several pieces of bread were in the store. Half of them plus a half of bread bought a cookbook. Of the remaining bread, half of it plus half of the bread was bought by Mr. Novák. The last bread was bought by Ms. Small. How many breads were in the store at.
15. Three friends
Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book?