# Examples of equations for high school

#### Number of problems found: 459

- Three groups

In the company, employees are divided into three groups. In the first group, which includes 12% of the company's total number of employees, the average salary is CZK 40,000, in the second group CZK 35,000, in the third group CZK 25,000. The average salary - Staircase

On a staircase 3.6 meters high, the number of steps would increase by 3 if the height of one step decreased by 4 cm. How high are the stairs? - Railway embankment

The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area. - Find d 2

Find d in an A. P. whose 5th term is 18 and 39th term is 120. - There

There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a - Kohlrabies

The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros. - Area and perimeter of rectangle

The content area of the rectangle is 3000 cm^{2}, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle. - Isosceles triangle

In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Journey to spa

Mr. Dvorak took his wife to the spa and the journey took 3.5 hours. On the way back, he drove 12 km/h faster and was home in 3 hours. At what speed did he go to the spa and at what speed did he return? - Find the 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - Quarantine cupcakes

Mr. Honse was baking quarantine cupcakes. Mrs. Carr made twice as many as Mr. Honse. Ms. Sanchez made 12 cupcakes more than Mr. Honse. If they put all their cupcakes together (which they can’t because. .. quarantine!) they would have 108 cupcakes. How may - The cylinder

The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder. - 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. - Finite arithmetic sequence

How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117? - Summands

We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands. - Right triangle - ratio

The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - 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 5 more double columns than three columns. How many students are in the class? - In the dairy

There were three times more packages of milk in the dairy than half a liter. When sold 10 liter and ten half-liter containers, four times more liters remained than half-liter packages. How many packages were there originally? - Circle and square

An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD. - Magnified cube

If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm^{3}. Determine the surface of both the original and the magnified cube.

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