The most difficult problems

  1. The tax
    fuel The tax per gallon of gasoline in California is $0.477. If you fill your gasoline tank with 14.4 gallons of gasoline in California, how much will you pay in taxes? Round to the nearest cent.
  2. An animal shelter
    cat An animal shelter spends $5.50 per day to care for each bird and $8.50 per day to care for each cat. Nicole noticed that the shelter spent $283.00 caring for birds and cats on Wednesday. Nicole found a record showing that there were a total of 40 birds an
  3. A rectangle 2
    rectangles A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
  4. Heptagonal pyramid
    truncated_hexagonal_pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.
  5. Coordinates of square vertices
    rotate_square I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
  6. Positional energy
    energy What velocity in km/h must a body weighing 60 kg have for its kinetic energy to be the same as its positional energy at the height 50 m?
  7. The hemisphere
    naklon_koule The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
  8. A concrete pedestal
    frustum-of-a-right-circular-cone A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
  9. Floating of wood - Archimedes law
    balza05 What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m3 and a volume of 0.02 m3 that floats in alcohol? (alcohol density is 789 kg/m3)
  10. Frustum of a cone
    cone-frustrum A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
  11. Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
  12. Propeller
    Tupolev_Tu-95 The aircraft propeller rotates at an angular speed of 200 rad/s. A) What is the speed at the tip of the propeller if its distance from the axis of rotation is 1.5 m? B) What path does the aircraft travel during one revolution of the propeller at a spee
  13. Reducing balance method
    books A company buys an item having a useful life of 10 years for 1,000,000. If the company depreciates the item by the reducing balance method, a. Determine the depreciation for the first year. b. Estimate the depreciation for the second and third years. c.
  14. A baker
    pie A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie. How many pieces of pie does she have?
  15. Compound interest 3
    exp_growth2 After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly? (interest is now dream - in the year 2019)
  16. Hole's angles
    Trapezium2-300x199 I am trying to find an angle. The top of the hole is .625” and the bottom of the hole is .532”. The hole depth is .250” what is the angle of the hole (and what is the formula)?
  17. Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  18. Geography tests
    test On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
  19. 3 phase load
    3phasesPower Two wattmeters are connected to measuring power in a 3 phase balanced load. Determine the total power and power factor if the two wattmeters read 1000 watts each (1) both positive and (2) second reading is negative
  20. The sum 4
    clocks The sum of Robin's age is 45. Seven years ago, Robin was 16 years more than one half as old as Bruno then. How old is Bruno?

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



We will send a solution to your e-mail address. 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...