# Algebra - problems - page 66

1. Electricity consumption cost
Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago?
2. Bag
Nelly found interesting point. An empty bag weighs 4 kg less than full. And empty bag is 5 times easier than full. How many kg weigh things in this bag?
3. Cylinder
In a 1-meter diameter cylinder is 1413 liters of water, which is 60% of the cylinder. Calculate the cylinder height in meters, do not write the units. The resulting value round and write as an integer.
4. Difference of two number
The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers.
5. Friends
James and Jaroslav are friends. Together they had 48 toy cars. But if John took 8 cars from Jaroslav, Jaroslav will be have 1.5 times more toy cars than James. How many toy cars had Jaroslav and James?
6. Biketrial
Kamil was biketrial. Before hill he set the forward gear with 42 teeth and the back with 35 teeth. After how many exercises (rotation) of the front wheel both wheels reach the same position?
7. AP - simple
Find the first ten members of the sequence if a11 = 132, d = 3.
8. Truck and car
At 6h45min the truck started at a speed of 36 km/h. At 7h30m behind it a passenger car. Find the average speed of passenger car if it will catch truck 72 km away from the factory.
9. Summer camp
Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing. Use a two-way table to organize the information and answer the following questio
10. Sawmill factory
Peter works in the factory. The bus stop is 10 km from the factory. Therefore, always when the bus arrives for Peter, the driver leaves factory and takes him to work. They are coming at the saw exactly at 8:00. Today the bus arrived 11 minutes earlier and.
11. EQ2
12. Parallelogram
Side a of parallelogram is twice longer than side b. Its circumference is 78 dm. Calculate the length of the sides of a parallelogram.
13. Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
14. Surface of cuboid
Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
15. Trees
A certain species of tree grows an average of 0.5 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
16. Alcohol
How many cubic centimeters of 96% alcohol is needed to obtain 0.75 liter of 40% alcohol?
17. Three monks
Three medieval monks has task to copy 600 pages of the Bible. One rewrites in three days 1 page, second in 2 days 3 pages and a third in 4 days 2 sides. Calculate for how many days and what day the monks will have copied whole Bible when they begin Wednesd
18. Tram lines
Trams of five lines driven at intervals of 5,8,10,12 and 15 minutes. At 12 o'clock come out of the station at the same time. About how many hours again all meet? How many times have earch tram pass for this stop?
19. AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
20. Land areas
Two land areas is 244 m2. The first parcel is 40 m2 less than twice of the second one. What have acreage of each parcel?

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