Quadratic equation + natural numbers - math problems

Number of problems found: 17

The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.
Find two
Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
1 page
1 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?
Two grandmothers
Two grandmothers went to sell eggs at the market, and they had a total of 100. When they sold all the eggs, they made the same money. The first grandmother says to the second: "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmot
Sequence
In the arithmetic sequence is given: S_n=2304, d=2, a_n=95 Calculate a₁ and n.
How many
How many different rectangles with integer page lengths have an area S = 60 cm²?
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?
Four integers
Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
Rectangle diagonals
It is given rectangle with area 24 cm² a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
Euler problem
Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
Tourists
Tourists hire a guide. Everyone will pay the same amount. If there are two less 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.
Loan 5
Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out the loan? C
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 the number 2430. What is the original two-digit number?
Lookout tower
How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
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.
Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm². Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
TV competition
In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We g