Integer equation - high school - practice problems - page 3 of 4
Number of problems found: 68
- Coefficients 4445
Find all triplets P (x) = a * x² + b * x + c with the integer coefficients a, b, and c to which it applies P (1) - 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. - Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
- Unknown 2881
Find an unknown number: (9 + y) x 6 = 12 x 7 y =? - Grandfather's 2876
To the question: How old are your two grandchildren? The grandfather answers: if I add their sum to the product of the numbers that determine their age, I get 14. How many years have grandfather's grandchildren? Think only for years. - Horses 2773
Horses, sheep, and ducks graze in the meadow. Sheep are more than ducks. Sheep and ducks have a total of 100 heads and legs. Ducks and sheep are three times more than horses. How many horses are there? - Remembered 2766
Aunt bought 6 identical mugs and one coffee pot. She paid €60 in total. A teapot was more expensive than one mug but cheaper than two mugs. Auntie remembered that all the prices were in whole euros. How much € was one mug, and how much was a kettle? - Banknotes
$ 1390 was collected. How much was in $20 notes, and how many in $50 notes in that order? How many solutions exist?
- Tangerines 2508
Michael, Tono, Marek, and Julia have 48 mandarins. Michael has 12 tangerines more than Tono, and Julia has eight tangerines less than Marek. Determine how much each has. - 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 - 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? - 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. - Friends
Some friends had to collect the sum of 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
- Digits A, B, C
For the various digits A, B, and C is true: the square root of the BC is equal to the A, and the sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product). - Scouts
Scouts purchased camp cans of two types total cost of 1460 CZK. The first cans were for CZK 32 and the second for 25 CZK. How many cans were purchased for each type? - 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? - Mushrooms from the forest
Magda and Tereza go to pick mushrooms. Found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms were found, Magda? - Sinus
Determine the smallest integer p for which the equation 4 sin x = p has no solution.
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