# Algebra - problems - page 33

1. Apples and pears
Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child?
2. Every day 7 pages
Adelka reads the book every day 7 pages. When she reads one more page a day she will read it three days earlier. How long will Adelka read a book? How much does a book of pages have?
3. Tractor wheels
Smaller tractor wheel has a circumference of 3 meters, bigger 4 meters. On what path executes smaller wheel 6 turns over more bigger?
4. Water in aquarium
The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water.
5. Swimming pool
The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
6. Medians in triangle
Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm.
7. Right angled triangle 2
LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
8. Buses
Buses Ikarus and Karosa simultaneously started at 8:00 from the final station. Ikarus is returned to the station after 30 minutes. Karosa after 45 minutes. At what time both buses again returned to the station?
9. Container with water
The weight of a container with water is 2.48 kg. If the cast 75% water, the container with water has a weight of 0.98 kg. Determine the weight of the empty container. How much water was originally in the container?
10. Triangle ABC
Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
11. The city 2
Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%?
12. College
At the college are at 57 rooms 194 students. Some rooms are triple and some quad. How many triple and quadruple rooms there is, if it is all fully occupied?
13. Rings groups
27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups?
14. Plums
In the bag was to total 136 plums. Igor took 3 plums and Mary took 4/7 from the rest. How many plums remained in the bag?
15. Divisibility 2
How many divisors has integer number 13?
16. Water reservoir
The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?
17. Probabilities
If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
18. Pumps
First pump flows 16 liters per second into the basin by the second pump 75% of the first and by third pump half more than the second. How long will take fill basin by all three pumps simultaneously volume 15 m3 (cubic meters)?
19. Direct route
From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t
20. Harvesters
The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first?

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