Integers + equation - practice problems - last page
Number of problems found: 93
- 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 - Proof I
When added to the product of two consecutive integers larger one, we get the square larger one. Is this true or not? - Find x 2
Find x, y, and z such that x³+y³+z³=k for each k from 1 to 100. Write down the number of solutions.
- The perimeter
The perimeter of the triangle is 24, and the sides are integers and form an arithmetic sequence. Specify the side sizes of this triangle. - Points on circle
The Cartesian coordinate system with the origin O is a sketched circle k /center O; radius r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points on the circle I with center O and radius r=5 cm, whose - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - When will I be a millionaire?
Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures are ignored.
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