Equation - high school - math problems

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?
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 cm³. Determine the surface of both the original and the magnified cube.
Birthdays
In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
Working together
Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone?
An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm³ if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
Growth of wood
The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
Three faces of a cuboid
The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
Mortage hypo loan
The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?
Hiking trail
The newly built hiking trail leads 25% through the field, 3/8 of the trail leads through the forest and the remaining 9 km along the river. How long is the train?
Vegetable meal
The cook was doing meal - in ratio 4: 3: 1 mix tomatoes: pepper: onion. Onions were 5 kg less than peppers. How many kgs of tomatoes did he need to prepare the meal?
Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
Water current
John swims upstream. After a while, he passes the bottle, from that moment he floats for 20 minutes in the same direction. He then turns around and swims back, and from the first meeting with the bottle, he sails 2 kilometers before he reaches the bottle.
The bridge
A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
Same force
The trunk of 5m length and 95 kilograms has a center of gravity 2m from the thicker end. The tribe is carried by two men, one at the thicker end. At what distance does the trunk carry a man from the other end to make the same force on it?