# System of equations - high school - math problems

#### Number of problems found: 356

- 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 - MF graduate

78 school students graduate from mathematics or physics. There are three times more students who graduate from mathematics and do not graduate from physics than those who graduate from physics and do not graduate from mathematics. 69 students graduate fro - 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? - The water barrel

The water barrel weighs 122 kg. If we pour 75% of the water out of it, it will weigh 35 kg. What is the weight of the barrel? - Part-time workers

Three part-time workers received CZK 1,235 for their work. The first received 20% less than the second and the third received 45 CZK more than the second. Determine how many crowns (CZK) each of them received. - Dimensions of the trapezoid

One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm^{2} - Line intersect segment

Decide whether the line p : x + 2 y - 7 = 0 intersects the line segment given by points A[1, 1] and B[5, 3] - 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]. - Triple and quadruple rooms

Up to 48 rooms, some of which are triple and some quadruple, accommodated 173 people so that all beds are occupied. How many triple and how many quadruple rooms were there? - Vector v4

Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - 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 - 2 cyclists and car

One cyclist rides at a constant speed over a bridge. It is 100 meters long. When he is 40 meters behind him, he meets an oncoming cyclist who is riding at the same speed. The car travels along the bridge in the same direction as the first cyclist at a spe - Candles

Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo - 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.

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