Equation - math word problems

  1. Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  2. Vector perpendicular
    3dperpendicular Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
  3. Vector equation
    collinear2 Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
  4. Ducats
    dukat The king divided the ducats to his three sons in a ratio of 2: 5: 4. How many ducats the king divided them if the youngest received 260 ducats, which was the least of all sons.
  5. Cuboid and ratio
    cuboid_2 Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
  6. Large family
    family I have as many brothers as sisters and each my brother has twice as many sisters as brothers. How many children do parents have?
  7. Runners
    runners If John has a running speed of 3.5miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 am and Lucy starts running at 10:30 am, at what time will they meet? (as soon as possible)
  8. Volume of wood
    wood Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
  9. Growth of wood
    wood The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
  10. Aircraft angines
    aircraft-02 The two engines of the aircraft are enough to supply the fuel for five hours of operation. However, one of the engines has a malfunction and thus consumes one-third more fuel. How long can the plane be in the air before it runs out of fuel? After an hour
  11. Three faces of a cuboid
    cuboid The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
  12. Mortage hypo loan
    hypo The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?
  13. Water container
    cubes2 The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
  14. Alcohol mixing
    roztoky_1 How much 64% of the alcohol must be poured into 6 liters of 85% alcohol to produce 79% alcohol?
  15. Hiking trail
    mapa The newly built hiking trail leads 25% through the field, 3/8 of the trail leads through the forest and the remaining 9 km along the river. How long is the train?
  16. Nádoba
    cube_sphere_in Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby?
  17. Vegetable meal
    paprika The cook was doing meal - in ratio 4: 3: 1 mix tomatoes: pepper: onion. Onions were 5 kg less than peppers. How many kgs of tomatoes did he need to prepare the meal?
  18. Suppose
    linear_eq Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
  19. Water current
    river John swims upstream. After a while, he passes the bottle, from that moment he floats for 20 minutes in the same direction. He then turns around and swims back, and from the first meeting with the bottle, he sails 2 kilometers before he reaches the bottle.
  20. Buttons
    oblek Men's shirt has sewn 9 buttons and blouse 3 buttons. Together they sewed 60 pieces and consumed 390 buttons. How many shirts?

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