Integer equation + reason - practice problems
Number of problems found: 115
- Solution 83099
There are spiders and flies on the window. They have a total of 38 legs. How many spiders and flies are there if a spider has 8 legs and a fly has 6? Just give one solution. - Two-digit 82521
Karel had to multiply two two-digit numbers. Out of care, he changed the order of the digits in one of the factors and got a product that was 4,248 less than the correct result. What is the correct result? How much should Karl have earned? - Position 81987
Find a number with six digits. If you put the last digit before the first, you get a new number that is five times larger. The digits between must not change their position. - Multiply 80797
When I multiply two equal natural numbers, I get the same result as when I add them together. Which ones are they?
- Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - 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.) - Arranged 80453
There are 390 trees arranged in rows in the orchard. How many rows are there if each row has the same number of trees greater than 30 and less than 40? - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number.
- Completely 79274
Kitchen cabinets are sold in widths of 80 cm, 60 cm, and 40 cm. Which assembly can we choose if we have a wall 3.5 m long and we want to completely fill it with an assembly that also includes a dishwasher, the width of which is 60 cm, and the stove is 50 - Three flocks
Flocks of birds pass by, and one bird on a tree asks them, how many of you? And they respond, we are so plenty. The second flock of birds again passes by and asks the bird on a tree, how many of you? The response is we are one-half (1/2) of the first floc - Rectangles 70304
How many rectangles with side lengths expressed in natural numbers have an area of 96 cm²? - Number 69614
The house has two floors. Men and women live on each floor in such a number that their ratio is 3:2 on each floor. Five more people live on the second floor than on the first floor. How many women live on the second floor? - Circumference 66964
We have to construct a rectangle with a circumference of 30 decimetres. The rectangle has sides of whole decimetres. How many different rectangles can we make?
- Conditions 66544
I have a box that contains white, milk, and dark chocolate candies. The ratio of white to milk candies is 3:4. The ratio of white to dark candies is 4:3. The least amount of candies in the box if the conditions of the ratio of candies are met. - Prepared 66494
Benches were prepared around the fire. When seven tourists sit on them, one tourist will sit alone on the last bench. When six of them all sat down, one had to stand. How many tourists were at the campfire if we know there were less than 100, and how many - Increased 64324
The number of books in the city library increased by 0.2% in 2008 and 0.6% in 2009. At the same time, the total number of books remained less than 300,000. How many books were added to the city library in 2009? - Three dices
What is the probability that the sum of points 14 will be a roll of three dice (B, M, Z)? - Squares
From the square with the integer side, cut out the square with the integer side so that the residual area is 100. What is the longest possible side of the larger square?
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