# Equation - examples - page 43

1. Ratio of sides
The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
2. Prove
Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
3. Farmland
Farmers seeded maize to 45 ha, which is 15% of their total farmland. How many hectares of fields they have?
4. Equation with x
Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9
5. Tea mixture
Of the two sort of tea at a price of 180 CZK/kg and 240 CZK/kg we make a mixture 12 kg that should be prepared at a price of 200 CZK / kg. How many kilos of each sort of tea will we need to be mixed?
6. Equation with abs
Solve this equation with absolute value member: ?
7. Solutions, mixtures
How many liters of 70% solution we must add to 5 liters of 30% solution to give us a 60% solution?
8. Dried fruit
The manufacturer produces a mixture of dried fruit. He purchased: 10kg pineapple for 200 Kc/kg 2kg papaya for 180 kc/kg 1kg of banana for 400 Kc/kg How many kgs of raisin for 80 Kc/kg must be put into the mix by the manufacturer so that the production pr
If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book?
10. Simple equation 3
24 = n • 27, solve for n
11. Flying
The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
12. Sphere equation
Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
13. Repair pipe
20 workers had to repair broken pipes in 30 days. After fourteen days, four laborers joined them. How long did the pipe repair work last?
14. Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
15. Hotel
The rooms in the mountain hotel are double and triple. Double rooms are 25 and triple are 17 more. How many rooms are there in this hotel?
16. Tractors
Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately?
17. The third
The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod?
18. Two pumps
Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself?
19. Four workers
Four workers will lay the floor of the gym in six hours. After an hour of working together, one of the workers left to the doctor. How long before the remaining three workers finish their work?
20. The work
The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take?

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