Natural numbers + quadratic equation - practice problems
Number of problems found: 28
- Pagans
Jano and Michael ate pagans. Jano ate three more than Michael. The product of their counts (numbers) is 180. How many pagans did each of them eat? - Solve: 6632
For n ϵ N solve: 100 = (0.01n)² - Consecutive 6402
The product of two consecutive natural numbers is 46 less than the product of the other two consecutive natural numbers in a row. Identify unknown numbers. - Two grandmothers
Two grandmothers went to the market to sell eggs, and they had 100. When they sold all the eggs, they made the same money. The first grandmother said to the second, "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmother replied - 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 - Determine 25341
In a two-digit number, the number of tens is three more than the number of ones. If we multiply the original number by a number written with the same digits but in the reverse order, we get the product 3 478. Determine the actual number. - Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now. - Loan 5
Abdul takes a loan of 200000 from Ali and agrees to repay in several installments. Each installment begins with the 2nd exceeding the previous one by 1000. If the first installment is 500, find how many installments will be necessary to be wiped out of th - 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. - Tourists
Tourists hire a guide. Everyone will pay the same amount. If there are two fewer of them, they will pay 14 crowns more, and if there are three more, they will pay 14 crowns less. How many tourists are there and how much have the guides paid? - 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? - Euler problem
Someone buys 300 tolars towels. If it were for the same money of 5 more towels, it would be 5 tolars cheaper each. How many were towels? - Four integers
Find four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two. - Find two
Find two consecutive natural numbers whose product is one larger than their sum. Searched numbers are expressed by a fraction whose numerator is the difference between these numbers, and the denominator is their sum. - 1 page
One page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book? - The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - Variations 70724
If we increase the number of elements by 2, the number of variations of the second class without repetition increases by 22. How many elements do we have initially? - Sequence
The arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n. - Difference 7159
The product of two natural numbers is 323, and their difference is 2. Determine the numbers. - Rectangle diagonals
It is given a rectangle with an area of 24 cm² and a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
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