Integers + integer equation - practice problems - page 2 of 3
Number of problems found: 43
- Legs
In the room are four-legged chairs and three-legged stools, and all are fitted with (one) person. I counted all the legs in the room, and there were 39. How many are there chairs, stools, and people? - Modulo
Find x in the modulo equation: 47x = 4 (mod 9) Hint - read as what number 47x divided by 9 (modulo 9) give remainder 4. - Diofant 2
Is equation 70x +52y = 34 solvable on the set of integers Z? - Integer
Find the integer whose distance on the numerical axis from number 1 is two times smaller than the distance from number 6.
- An integer
An integer is 17 more than five times another. If the product of the two integers is -6, then find the integers. - Endless lego set
The endless lego set contains only 6, 9, and 20-kilogram blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And, of course, they wrote down how much the building weighed. - Rectangle
The perimeter of the rectangle is 22 cm, and the area is 30 cm². Determine its dimensions if integers express the length of the sides of the rectangle in centimeters. - 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 - Centimeters 5681
The triangle has side lengths expressed in whole centimeters. One of them measures 8 cm, and the sum of the remaining two sizes is 32 cm. Determine the lengths of the remaining sides. Find all solutions.
- Line
Straight-line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line in which both coordinates are positive integers. - Together
If eight men, ten women, and 16 children collect ₹1024 in 4 days, how many days will be required for six men, five women, and four boys to collect ₹768? (₹ is Indian Rupee) - Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Sugar - cuboid
Pablo received from his master a cuboid composed of identical sugar cubes with a count between 1000 and 2000. The Pejko eat sugar cubes in layers. On the first day, eat one layer from the front. On the second day, one layer from the right, and on the thir
- Repairman
The repairman has vowed to do repair work at the plant for 25 days. However, work had to be shortened, so he took a helper worker. Together they made all the corrections for the whole day. How long would it take work to help workers? - 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.) - Banknotes
$ 1390 was collected. How much was in $20 notes, and how many in $50 notes in that order? How many solutions exist? - Positive 7040
Find all positive integers x and y for which: 1 / x + 1 / y = 1/4
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