Reason - math word problems - page 14 of 108
Number of problems found: 2157
- Integer part system
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Triangle circle proof
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri - There 26
There are 200 sweets in a jar, measured to the nearest 10. They weigh 600 grams to the nearest 10 grams. What is the least possible mass of each sweet in grams? 2 d. p - Rose bouquet maximum
At the flower shop, they received 72 white roses and 96 red roses. What is the maximum number of bouquets they can tie to all these roses if each bouquet is to have the same number of white roses as red roses? - Digit omission divisibility
In the number 123 456 789, omit the following: a) one digit to create the largest possible number divisible by 3 b) one digit to create the largest possible number divisible by 9 - Orchard tree rows
There are 390 trees arranged in rows in the orchard. How many rows are there if each row has the same number of trees greater than 30 and less than 40? - Family visit count
Dulikovci, Elikovci, Filikovci, and Galikovci visited each other often last month. Each family visited each family exactly once. How many visits did all four families make together? If two families came to visit one family simultaneously, count it twice. - Number inequality replacement
What is the smallest whole number to replace the known x for: 9> x/3> 4. - Six-digit number creation How many six-digit numbers without repetition can be formed from the digits 1, 2, 3, 4, 5, and 6, if the numbers are, to begin with: a) the digit 4; b) digits 4 or 5?
- Number symmetry divisibility Complete the digits to create a symmetrical number divisible by 5 to the number 346.
- Apple bowl remaining
There were 10 apples in the bowl. There were 35 apples in the bucket. Ivan transferred 15 apples from the bucket to the bowl. Then Zora took 4 apples from the bowl. Mom took 2/3 of the remaining apples in the bowl for the pie. How many apples are left in - Boy tablet dosage
Pepík is sick and has to take 1 tablet three times a day. How many days will a pack of 30 tablets last him if he only takes 1 tablet in the morning and evening every third day? - Reconstruction The school decided to carry out a reconstruction and wanted to start by replacing the doors. After installing the doors, the principal decided to mark each door with numbers. As soon as he got this idea, he had mathematicians calculate how many digits the
- Five-digit number divisibility How many different five-digit numbers with different digits can be made from the digits 0, 2, 4, 6, 7, 8, and 9? How many of them are divisible by 4? How many of them are divisible by 10? How many of them are even?
- Five-digit number count Determine the number of all natural numbers greater than 2000 in which the digits 1, 2, 4, 6, and 8 occur at most once each.
- Village railway distance
The picture shows three villages, A, B, and C, and their mutual air distances. The new straight railway line is to be built so that all the villages are the same distance from the line and that this distance is the smallest possible. How far will they be - Cube wall coloring
We color a wooden cube with an edge length of 3 cm so that three walls are blue, three are red, and no two opposite walls are the same color. Cut the cube into 1 cm³ cubes. How many cats will have at least one red wall and at least one blue wall? - Tennis ball parabola
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - Number digit formation How many numbers a) less than 500, b) greater than 500 can be formed from the digit 0,1,5,8,9 so that no digit is repeated?
- Dance pair duration
Thirty-two boys and 34 girls came to the dance. How many different dance pairs can they make, given that each team is given: they can only dance for 1 minute and then take turns in 5 seconds? Calculate how long the dance evening would last for all the pai
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