# Algebra - problems - page 86

- MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Triangles

Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have? - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm^{2}and side is 13 cm long. - The tank

The tank had 9 inflows to be filled in 21 days. After 9 days, 3 trips out. How many days did the remaining 6 tributaries fill the tank? - Bricks pyramid

How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid? - Rectangles

The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle? - Budget plan

In the construction of the building, the planned budget exceeded 13%, which was 32,500 euros. How many euros cost built the building? - Cuboid walls

If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid. - Linsys2

Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144 - Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm - Workers

Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send? - Parking

At a building parking, 245 spaces are for cars, 56 are for vans and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses? - Cakes

1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes? - One kilogram

The apple weighs 125 grams and half apple. How many apples weigh 1 kilogram? - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Triangle perimeter

Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long. - Soldier

An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together? - Tractors

5 tractors will plow the field for 8 hours. In 2 hours, 1 tractor broke down. How long do the remaining tractors complete the plow? - Three points 2

The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. - Discount

The dress was discounted by CZK 115, which was 12% of the original price. What is the cost of the dress after the discount?

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