# Integers - 9th grade (14y) - examples

1. Simplify
Simplify expression - which expression is equivalent to: 3(m + 2) − 4(2m − 9)
2. Collection of stamps
Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
3. Monkey
Monkey fell in 23 meters deep well. Every day it climbs 3 meters, at night it dropped back by 2 m. On what day it gets out from the well?
4. Diofant 2
Is equation ? solvable on the set of integers Z?
5. 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)
6. Dice
How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
7. Sequence
In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
8. 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
9. Shooter
The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
10. Rectangle
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.
11. Line
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.
12. Monty Hall
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books?
14. Package
The package has no more than 67 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 3.8 m of cloth and on one dress 1.7 m. Determine the amount of the cloth in the package.
15. Gauss
Help little C.F. Gauss sum all the integers from 1 to 400.
16. Legs
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?