# Algebra - problems - page 85

1. 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.
2. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
3. 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?
4. Cakes 1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes?
5. Repay, interest, loan Ramchacha takes a loan amount of 240000 from a bank for constructing a house at the rate of simple interest of 12% per annum. After 1 yr. of taking the loan he rents the house at the rate of 5200 per month. Determine the number of years he would take to re
6. Linsys2 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
7. 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?
8. 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?
9. 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?
10. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
11. One kilogram The apple weighs 125 grams and half apple. How many apples weigh 1 kilogram?
12. Triangle perimeter Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
13. 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? Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
15. The Hotel The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r
16. 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?
17. 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.
18. 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?
19. I think I think a number. When I multiply it by five, and after that I subtract 477, I get the same number as if I multiplied it twice. What number do I think?
20. Temperature 2 Sunday's high temperature was 3 degrees higher than Saturday's. On Monday, the temperature fell 5 degrees, then rose 7 degrees on Tuesday and 4 more on Wednesday. Then it fell 17 degrees to a record low of 31 on Thursday. What was the temperature on Saturd

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