# Algebra - problems - page 30

1. Pair
They have together 39 years - he has 2 times as she was when he was equal as she has today ....
2. Homework
Mother and Kate together weigh 24.5 kg more than the father. Father weighs 7.6 kg more than mother. Father weight 44.8 kg more than Kate. Determine weights of father mother and Kate.
3. Three shapes
1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
4. Lenka and money
When Lenka bought pants from 1/3 of her savings shirt from 1/5 and 1/8 spent at the hairdresser, she is left 328 Kč. How much money was saved? How much hairdresser cost?
5. Water pool
Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
6. Orchard
Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou
7. Blackjack TU160
Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At
8. Triangle
For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
9. Diameter
What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
10. Tetrahedral prism - rhomboid base
Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
11. Divisors
The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
12. Mixing
If we mix 5 kg of goods of one kind and 3 kg second one, resulting mixture cost 16.50 EUR/kg. If these quantities are mixed in reverse - first three kilograms and 5 kilograms second cost of mixture is 18.50 EUR/kg. What is the price of one kg of goods of.
13. Tippler
Bottle with cork cost 8.8 Eur. The bottle is 0.8 euros more expensive than cork. How much is a bottle and the cork?
14. Semicircle
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
15. Decomposition
Make decomposition using prime numbers of number 155. Result write as prime factors (all, even multiple)
16. Two wine
In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine?
17. Three digits number
From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
18. Exponential equation
Solve exponential equation (in real numbers): 98x-2=9
19. Coordinate
Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5x
20. Circle chord
Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.

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