Integer equation - practice problems - page 9 of 10
Number of problems found: 194
- Mug and kettle
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? - Candy cost
Two bars and one candy cost 24 CZK. Two candies and one bar cost CZK 27. How much does candy cost? - Tangerine distribution
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
In a Cartesian coordinate system with origin O, a circle k is drawn with centre O and radius r = 2 cm. Write all points on circle k whose coordinates are integers. Write all points on the circle with centre O and radius r = 5 cm whose coordinates are inte - Repairman
A repairman promised to complete repair work at the plant in 25 days. However, the work had to be shortened, so he took on a helper. Together, they finished all the repairs in a full day. How long would the helper take to do the work alone? - 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. - Daughters
The man conducting the census asks a woman the age of her three daughters. The woman says when multiplying the age, get the number 72; if their ages add up, get a number of our house, as you see. The man says: That is not enough to calculate their ages. S - 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? - Basements
In the first cellar, there are more flies than spiders. In the second, the opposite. In each cellar, the flies and spiders had a combined 100 legs. Determine how many flies and spiders could have been in the first and how many could have been in the secon - 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). - Three co-owners
The three co-owners of the building company have earnings from a contract portioned in the ratio of 3:6:7. Each of them received the amount in the whole USD. One of them, on contract, earned 86450 USD. What were the total earnings for this order? - Scouts
Scouts purchased two types of camp cans for a total cost of 1460 CZK. The first can cost CZK 32, and the second cost 25 CZK. How many cans were purchased for each type? - Legs
There are four-legged chairs and three-legged stools in the room, all fitted with (one) person. I counted all the legs in the room, and there were 39. How many chairs, stools, and people are there? - Cooks
Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cooks would have to work cleaning 9 kg of potatoes for 12 minutes? - Mushrooms from the forest
Magda and Tereza go to pick mushrooms. Found 70 mushrooms. Magda found that between fungi, 5/9 bedel was found. Tereza discovered that she found 2/17 champignons among fungi. How many mushrooms were found, Magda? - Cottages
The summer camp has 41 cottages. Each has rooms for three and four. How many of the 140 campers live on three? - Sinus
Determine the smallest integer p for which the equation 3 sin x = p has no solution. - 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.
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