# Equation + system of equations - math problems

1. 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?
2. The circumference The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
3. Side lengths In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
4. The four The four pirates divided 65 coins to each other. They were sorted by age, the youngest receiving the least number of coins, each half more than the previous one. How many coins did the oldest pirate receive?
5. In a In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
6. 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?
7. 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?
8. Sweets, candy Grandfather gave out sweets to four children. At the last moment, two more children came, so in order to have them all the same, each of the four children would receive four candies less than they would have received if they had not. How much did my grand
9. In the classroom There are 30 boys and a few girls in the class. In the six months, 28 boys and all girls benefited, which was 95% of all pupils. How many pupils are there in the classroom?
10. Block or cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
11. 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)
12. 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
13. Tourist cottage The tourist cottage has 11 rooms for 16 guests, some of them are doubles, some singles. How many are double rooms and how many are single rooms?
14. Two gardens The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?
15. Twelve ties The price of 12 ties before the discount was the same as 15 ties after discount. Calculate the price of 1 tie after discount, if you know that the discount price of one tie fell by 40 CZK?
16. Large family I have as many brothers as sisters and each my brother has twice as many sisters as brothers. How many children do parents have?
17. 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.
18. 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?
19. 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.
20. Buttons Men's shirt has sewn 9 buttons and blouse 3 buttons. Together they sewed 60 pieces and consumed 390 buttons. How many shirts?

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