# Algebra - problems - page 50

1. Sweets
3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations
2. Jam cakes
Mom baked a third of plum jam cakes, one third cheesecakes and 18 poppy. How many cakes she had bake?
3. Cenda and Pepa
Cenda and Pepa went to the event. Cenda started alone. Canda started after him for 20 minutes. How long took Cenda to catch him? Cenda traveling at 15 km/h, and Pepa traveling at 25 km/h.
4. Cork and swimming
If a person weighs 80 kg, how many kilograms of cork must take swimming belt to use it to float on water? The density of the human body is 1050kg/m3 and cork 300kg/m3. (Instructions: Let the human body and cork on a mixture that has a density of 1000kg/m
5. Cakes Z8-I-5
Mom brought 10 cakes of three types: kokosek was less than laskonek and most were caramel cubes. John chose two different kinds of cakes, Stephan did the same and for Margerith leave only the cakes of the same type. How many kokosek, laskonek and caramel c
6. Rectangle
The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?
7. Grandmother and grandfather
Grandmother baked cakes. Grandfather ate half, then quarter of the rest ate Peter and Paul ate half of rest. For parents left 6 cakes. How many cakes maked the grandmother?
8. Value
Determine the value of the following exspressions: a) (23-25)·(4-5) b) (97-123):(18+8)
9. Bicycle wheels
Driving wheel of a bicycle has 54 teeth. The driven wheel has 22 teeth. After how many revolutions will meet the same teeth?
10. Trams
Tram no. 3,7,10,11 rode together from the depot at 5am. Tram No. 3 returns after 2 hours, tram No. 7 an hour and half, no. 10 in 45 minutes and no. 11 in 30 minutes. For how many minutes and when these trams meet again?
11. Jan and Dan
Jan and Dan had the same money. Jan bought 5 workbooks and left him 15 CZK. Dan 6 and left him nothing. How much money have in total?
12. Cube 8
The surface of the cube is 0.54 m2. Calculate the length of the cube edge.
13. Cuboid - edges
The sum of all edges cuboid are 8 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid.
14. Bank
Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
15. Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
16. Barbara
Barborka goes to school with backpack that was 2 - times more expensive than a bag slipper. If backpack was 36 euros cheaper it was cost same as bag slipper. How many cost backpack and how many bas slipper?
17. Triangle KLM
In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
18. Two numbers
Determine the numbers x and y so x + y = 8 is truth and the numbers are in the ratio of 4: 5.
19. Average mark
Calculate average mark in English, if a student got a couple of 3's, 20% less 2 than 3, and 50% more 1's than the 2's.
20. Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?

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