Divisibility + system of equations - practice problems
Number of problems found: 17
- Prepared 66494
Benches were prepared around the fire. When seven tourists sit on them, one tourist will sit alone on the last bench. When six of them all sat down, one had to stand. How many tourists were at the campfire if we know there were less than 100, and how many - What is 16
What is the sum of three consecutive even integers such that six more than twice the second is 2/3 of the first increased by 3/2 of the third? - Consecutive 47011
The sum of two consecutive odd numbers is 184. What are these numbers? - Coloured numbers
Mussel wrote four different natural numbers with colored markers: red, blue, green, and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div
- Columns of two and three
When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are five more double columns than three columns. How many students are in the class? - 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 - Matemakak 9432
The cookbook by Matěj Matemakak says: The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest c - Mathematical 7034
Jaroslav and his grandfather often played mathematical games. His grandfather gave him the following puzzle: The sum of four consecutive even numbers is 116. What are they? - Candy and boxes
We have some candy and empty boxes. When we put ten sweets in boxes, there will be two candies and eight empty boxes left. When of eight, there will be six candies and three boxes left. How many candy and empty boxes are gone when we put nine sweets into
- Christmas 5740
When the mothers sat down on the benches at the Christmas gazebo, only one mother sat on the last bench. When the six of them sat down, one mother remained standing. How many mothers were there on the gazebo, and how many benches could they sit on? - Odd numbers
The sum of four consecutive odd numbers is 1048. Find those numbers. - Sales of products
For 80 pieces of two quality products, the total sales are 175 Eur. Suppose the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold? - Individual 4881
There are 32 rooms in the hostel. Some have double beds, others have four beds and the rest have 7 beds. There are a total of 139 beds in the hostel. How many are there if a two-digit number gives the numbers of individual species? - Have solution
The sum of four consecutive even numbers is 92. Determine these numbers.
- Beginning 2799
Three friends were playing bullets. They did not have the same number of marbles at the start of the game. They had them in a ratio of 2:7:5, while Mišo and Jano had a total of 77 bullets. How many marbles did their friend Peter have at the beginning? Cou - 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? - Grandson and granddad
Grandson with grandpa, they counted how many years have together. Their product is 365. How many years is the sum of their years?
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