# Algebra - math word problems

1. 2nd class variations
From how many elements you can create 2450 variations of the second class?
2. Tangents
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
3. Logarithmic equation
Solve equation: log33(3x + 21) = 0
4. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
5. Garden
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
6. Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
7. Two doctors
Doctor A will determine the correct diagnosis with a probability 93% and doctor B with a probability 79%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
8. Number ratio
Calculate two positive numbers that its ratio is 6:6 and difference was 0.
9. Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
10. Shape
Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books?
12. Playground
Rectangular playground is fenced with 38 m long netting. Its width is 7 m. Calculate its length.
13. Rectangle
Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
14. Computer revolution
When we started playing with computers, the first processor, which I remember was the Intel 8080 from 1974, with the performance of 0.5 MIPS. Calculate how much percent a year rose CPU performance when Intel 486DX from 1992 has 54 MIPS. Wha
15. Salary
Lawyer got to pay 840 Euros in banknotes of 20 and 50 Eur. Total got 18 banknotes. How many was which?
16. Square diagonal
Calculate the length of the square diagonal if the perimeter is 476 cm.
17. Chickens and rabbits
In the yard were chickens and rabbits. Together they had 14 heads and 44 legs. How many chickens and how many rabbits was in the yard?