Examples for 9th grade

  1. Four numbers
    equilateral_triangle_5 The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
  2. Repair pipe
    workers_39 20 workers had to repair broken pipes in 30 days. After fourteen days, four laborers joined them. How long did the pipe repair work last?
  3. Cube, cuboid, and sphere
    cubes3_8 Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
  4. Klara
    tourists_6 Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls?
  5. Triplets
    age_2 Three years ago, the triplets Pavel, Petr, and Luke and their five-year-old sister Jane had together 25 years. How old is Jane today?
  6. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  7. Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  8. Speed of car
    autosalon_2 The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
  9. Inscribed sphere
    cubes2_7 How many percents of the cube volume takes the sphere inscribed into it?
  10. Enlarged rectangle
    rectangle_10 The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
  11. Cancel fractions
    zlomky_15 Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
  12. Apples
    jablka_14 Zuzana bought 3 kg Jonathan apples. Then she noticed that Golden apples were 3 CZK a kilogram cheaper. So they bought 2 kg. For apples, she paid a total of CZK 109. How much did 1 kg Jonathan and how much Golden?
  13. Candy and boxes
    cukriky_13 We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of.
  14. Rhombus
    kosostvorec_1 The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
  15. Paul earned
    workers_35 Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t
  16. Ratio of sides
    trojuholnik_5 The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
  17. Overload
    aircraft-02_10 What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
  18. A triangle
    triangle1_1 A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
  19. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  20. Value 4
    fractal_11 If 5/18=425 what is the value 13/18?

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