Equation + reason - practice problems - page 3 of 37
Number of problems found: 735
- Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Introduced 81104
The * (asterisk) operation assigning one number to two pairs of numbers is introduced as follows: (a, b)*(c, d) = ac+bd We know that: (x,2)*(-1, v) = -1 and (2,-1)*(u, v)=5 and (u, v)*(1,1)=-2 What is (1,2)*(x, y) equal to if y=3? - Respondents 81024
Out of 32 people, 22 like fish. Four fewer people will enjoy the mushrooms. Those who eat mushrooms or fish are 7 times more than those who do not eat mushrooms or fish. How many of the respondents have fish and mushrooms? - Thanks 81022
Pavla is 2x older than Irena. Four years ago, Pavla was 6 times older than Irena was then. In how many years will the ages of Pavla and Irena be in the ratio of 4:3? Thanks
- Participants 80965
After the meeting, all participants shook hands with each other - a total of 105 times. How many people were there at the meeting? - Multiply 80797
When I multiply two equal natural numbers, I get the same result as when I add them together. Which ones are they? - Increases 80774
A bus travels between places A and B. If it increases its average speed by 5 km/h, the travel time will be reduced by 20 minutes. If he reduces his original speed by 4 km/h, the driving time is increased by 20 minutes. What is the average speed of the bus - Increases 80772 The product of two numbers we know. If we increase the first factor by 2 and decrease the second factor by two, the product increases by 4. How much does the product change if we decrease the first factor by 3 and increase the second factor by 3?
- Determine 80714 Three different numbers are given. The average of the average of two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers. The average of the smallest and largest number is 2022. Determine the sum of the t
- Single-digit 80674
There are cows, ducks, and geese on the farm. They have a total of 126 legs. Ducks are 3 more than houses. And there are 20 cows. If we count all the animals, we have to divide them by the number three, and we should get a single-digit number. - Grandchildren 80639 The average age of the grandfather, grandmother, and their five grandchildren is 26 years. The average age of the grandchildren themselves is 7 years. Grandma is a year younger than grandpa. How old is grandma?
- Smallest z9 Find the smallest positive numbers a and b for which 7a³ = 11b⁵
- Nightmares 80568
At the dream market, she offered the Sphinx to a traveler for four dreams, seven illusions, two naps, and one nightmare. Another has seven dreams, four illusions, four naps, and two nightmares. The Sphinx always measures the same for all travelers. How ma - Positive integer integral How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400?
- Differences 80551
Bolek and Lolek each had their own arithmetic sequence. Both Lolek and Bolek's sequence started with the number 2023 and ended with the number 3023. The two sequences had 26 numbers in common. The ratio of Bolek's and Lolka's difference was 5:2. What is t - Equations: 80499
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.) - Arranged 80453
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? - Smallest 80368
What is the smallest whole number to replace the known x for: 9> x/3> 4. - Parabolic 79764
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?
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