# Algebra - math word problems

1. 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.
2. 7 digit number If 3c54d10 is divisible by 330, what is the sum of c and d?
3. Flowerbed Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
4. 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
5. 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.
6. The painter In order for the painter to get the desired color, he must mix green and yellow in a ratio of 4: 7. If it has 28 l of green color, how many liters of yellow color should he add? How many liters of mixed color does he get?
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. Cakes 1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes?
9. 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?
10. 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
11. Linsys2 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
12. 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
13. 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?
14. 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?
15. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
17. One kilogram The apple weighs 125 grams and half apple. How many apples weigh 1 kilogram?
18. Triangle perimeter Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
19. 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?
20. 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?

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