# Algebra - math word problems

1. Parabola Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
2. Parachutists Parachutists during freefall firstly held in groups of 4, then of 6, then 9, 12 and finally of 18 members. How many parachutists jump at least should be, if at each group must all be involved.
3. Decimal to fraction Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
4. Geometric progression 2 There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
5. Geometric sequence In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
6. Legs In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
7. Book To number pages of thick book was used 4201 digits. How many pages has this book?
8. Scouts Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type?
9. QuizQ An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side?
10. Cars speeds Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
11. Cargo Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load?
12. Trapezoid 15 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
13. Three workers Three workers were rewarded CZK 9200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received?
14. Rectangle pool Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
15. Fewer than 500 sheep, There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?
16. Eva When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet?
17. Two months Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
18. Floor Rectangular floor of living room has a length 5.4 meters and a circumference 17.2 meters. What is its width?
19. Rings - intersect There are 15 pupils on the sporting ring. 10 pupils go to football, 8 pupils go to floorball. How many pupils go to both rings at the same time?
20. Arithmetic average The arithmetic mean of the five numbers is exactly 8. The sum of these four numbers is 30. What is the fifth number?

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