Integer equation + quadratic equation - practice problems
Number of problems found: 18
- A group
A group of young men decides to raise ksh 480,000 to start a business. Before the actual payment was made, four members pulled out, and each of the remaining had to pay an additional ksh 20,000. Determine the original number of members. - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - An integer
An integer is 17 more than five times another. If the product of the two integers is -6, then find the integers. - 11990 perimeter RT
A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length.
- A fraction
I think of a fraction. If we increase its numerator and denominator by one, the value of the fraction increases by one-tenth. What fraction do I think? - How many
How many different rectangles with integer side lengths have an area S = 60 cm²? - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - TV competition
In the competition, ten contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors who answered incorrectly in that round. After the contest, one of the contestants said - MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning, they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
- Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get 2430. What is the original two-digit number? - 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) - 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? - 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. - Primes 2
For what primes p,q,r is true: p²-(q+r)²=647
- 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? - Quadratic function
It is given a quadratic function y = -4x²+5x+c with an unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points. - Square Number
If to a square of integer number add 43, we get the square of the following integer number. What is the original number?
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