Algebra - math word problems

  1. MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  2. 7 digit number
    numbers2_49 If 3c54d10 is divisible by 330, what is the sum of c and d?
  3. Flowerbed
    flowers_9 Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
  4. Pyramid cut
    ihlan_rez 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
    cuboid_19 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
    painter_12 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
    digging_1 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
    buhty_1 1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes?
  9. Rectangles
    rectangle_15 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
    repay 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
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  12. The Hotel
    hotel-montfort-tatry-2_2 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
    penize_49 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
    workers_34 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
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  16. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  17. One kilogram
    jablka_19 The apple weighs 125 grams and half apple. How many apples weigh 1 kilogram?
  18. Triangle perimeter
    triangle_vysky_3 Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
  19. Parking
    cars_27 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
    tractors_2 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?

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...