# Reason + expression of a variable from formula - examples

1. Rectangle diagonals It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
2. Carpet The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag
3. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
4. ICE train German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys
5. One and a half chicken One and a half chicken bears one and a half egg in one and a half day. How many eggs can withstand from 6 chicken in 6 days?
6. Oil tank and pipes The underground oil tank can be filled by two oil pipelines. The first is filled in 72 hours and the second in 48 hours. How many hours from the moment when first pipeline began to fill the oil is it necessary to start filling it with the second to fill in
7. Direct route From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t
8. Trapezoid thirds The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
9. Disease Farmers'cooperative had a supply of feed for 50 cows to 6 days. Cows got insidious disease after 4 days, 10 of them died. How many total days that farmers had feed for cows?
10. MO-Z5-3-66 tiles The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.
11. 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?
12. Four swords Obelix has three helmets, four swords and five shields. How many swords must make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor?
13. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
14. Cuboid and ratio Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
15. Apples 5 In six crates are 45 kg of apples. In five crates were the same amounth and in one crate was 3 kg of apples more. How many kg of apples were in each crate?
16. Chairs Determine the number of seats in the seventh row and ninth row, if 3rd row has 14 seats and in every next row of seats has five more than the previous row.
17. Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
18. VAT on books The cost of a book in the store is 12.5 euros. How much euros is the VAT of this book? VAT is 10%.
19. Wine A bottle of wine costs 21 euros; and wine is 20 times more expensive than a bottle. How much a bottle cost?
20. Trucks Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks br

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