# Algebra - problems - page 42

1. Children
Less than 20 children is played various games on the yard. They can create a pairs, triso and quartets. How many children were in the yard when Annie came to them?
2. Alcohol 2
Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?
3. The port
Four ships Berthed in the port. Together sail from a port. The first ship will return to port every two weeks, second ship after 4 weeks, third after 8 weeks and fourth ship after 12 weeks. After how many weeks all the boats gather at the port?
4. Sugar cubes
The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured?
5. Tank 9
The tank with volume V is filled with one pump for three hours and by second pump for 5 hours. When both pumps will run simultaneously calculate: a) how much of the total volume of the tank is filled in one hour b) for how long is the tank full
6. Turtles Žofka and Julka
Gray wolf kept in his tent turtles Žofka and Julka, which together have 200 years. After 50 years will Julka 2 times older than Žofka. How old are the turtles?
7. Number
What number I think? The third is 6 and half is 2 more than the its quarter.
8. Sequence
Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
9. Three numbers
Create from digits 1-9 three-digit numbers with their sum the smallest. What value is the sum of these numbers? (Use each digit only once)
10. Painting school
Redecoration school had scheduled for four crew to 10 days. After two days a single worker ill. For how many days the school was painted when remain workers working with the same tempo?
Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
12. Classs mean
Class size is 30 students, math was not worse than sign 2. Determine the number of pupils who were sign 1 if the class had a 1.4 sign average.
13. Holiday SMS
Kucera and Malek start from the holiday together. They agreed that if they be 100 km apart, will send a SMS. Kucera traveling at 60 km/h., Malek 90 km/h. They started at 14 hours PM. At what time they send a message?
14. Copy typist
Typist for 12 hours rewritten 15% of the manuscript. After how many hours he will done 35% of the manuscript?
15. Internal angles IST
Determine internal angles of isosceles trapezium ABCD /a, c are the bases/ and if: alpha:gamma = 1:3
16. Seven tractors
Seven tractor plowed 308 ha field in four days. How many hectares of fields will plowe 9 tractors in 3 days at the same power?
17. Rhombus and diagonals
The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
18. Three friends
Peter is eight times older than Rado, Rado is 3 times younger than Joseph. Together they have 120 years. Determine how many are each of them.
19. Compound interest
Compound interest: Clara deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Both money and interest remain deposited in the bank. How many CZK will be in the bank after 3 years?
20. Alcohol mixing
How much 55% alcohol we must pour into 1500 g 80% alcohol to form a 60% alcohol? How much 60% alcohol created?

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