Integer equation - practice problems - page 5 of 9
Number of problems found: 178
- Sufficient 9391
In Kocourkov, they use coins with only two values expressed in Kocourkov crowns by positive integers. With a sufficient number of such coins, it is possible to pay any integer amount greater than 53 cats’ crowns accurately and without return. However, we
- Notebooks 8651
I need to buy exercise books and covers. One notebook costs CZK 12, and one cover costs CZK 3. I have one fifty crown and one twenty crown. How many notebooks and covers can I buy for it? Come up with more options.
- Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions.
- Observed 8276
We observed road traffic. We only saw bikes and cars. There were a total of 40 laps on the road. List at least three options how many bikes could be and how many cars?
- 102—likewise 8205
The number 20 137 is "like" the number 73 102—likewise, the decimal numbers 41.9 and 9.14, or 31.08 and 80.13, like each other. Find two mutually exclusive numbers whose product is 357.435.
- Several 8130
The hotel has 27 beds in several rooms. There are single, double and triple rooms. How many single, double and triple rooms can there be in the hotel? Give at least three options.
- Self-counting machine
The self-counting machine works exactly like a calculator. The innkeeper wanted to add several three-digit natural numbers on his own. On the first attempt, he got the result in 2224. To check, he added these numbers again, and he got 2198. Therefore, he
- 600 pencils
Six hundred pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
- Construction 7926
Honza had 19 wheels in the kit. He used all these wheels in the construction of tricycles and scooters. How much does he assemble complete scooters, and how many tricycles? Find all solutions.
- Education 7919
A total of 10 teachers work at one small school in Moravia. Their monthly salary is CZK 21,500, CZK 21,800, or CZK 22,500, depending on their education and age. The average monthly salary of a teacher at this school is CZK 21,850. How many teachers of thi
- Dimensions 7912
How many blocks have integer dimensions of the edges if the surface is 48 m²?
- Mathematics 7806
Janko has committed that his average grade in mathematics will be exactly 2 at the end of the semester. However, so far, he has received grades 3 and 4. He knows that by the end of the year, he will receive four more grades from the tests. What are the wo
- Grandmother
Mom walked out to visit her grandmother in a neighboring village 5km away and moved at a speed of 4km/h. An hour later, father drove down the same road at an average speed of 64km/h. 1) How long will it take to catch Mom? 2) What is the approximate distan
- There
There are two numbers on the screen - one in the blue and the other in the red box. In the beginning, both numbers are the same. With each beep, both numbers increase - by 1 in the blue field and by 3 in the red field. At one point, the number 49 appears
- Two-digit 7607
The digit sum of a two-digit number is 11. After changing the order of the digits, I get a number 27, smaller than the intended number. What number do I think?
- Consecutive 7550
The sum of four consecutive integers, five greater than the previous one, is 2. Find these numbers.
- The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor; no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
- Incorrectly 7484
Tomáš was given the task of solving 10 problems. He received 3 points for each correctly solved, and 4 points were deducted for each incorrectly solved. He scored a total of 9 points. How many tasks did he solve correctly, and how many incorrectly or not
- Chocolate
I have a box of chocolate - white, milk, and dark. The ratio of white to milk with dark is 3:4. The ratio of white and milk to dark is 17:4. Calculate the ratio between white, milk, and dark chocolate.
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