# Algebra - problems - page 16

1. Euler problem
Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
2. Count of roots
How many solutions has equation x. y = 7757 with two unknowns on the set of natural numbers?
3. Intersections
How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
4. Water container
Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container?
5. 3-bracket
May be the largest angle in the triangle less than 20°?
6. School books
At the beginning of the school year, the teacher gave out 480 books and 220 textbooks. How many students were in the class?
7. Gardens
The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
8. Two workers
Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker?
9. Rectangle
Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
10. Tiles
The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.
11. 9.A
9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
12. Segments
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
13. Family and age ratios
Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother?
14. Party
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
16. 2nd class combinations
From how many elements you can create 4560 combinations of the second class?
17. Geometric mean
Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
18. Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
19. Two runners
Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
20. Tiles
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.

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