9th grade (14y) + system of equations - examples

  1. Supermarket 2
    pie_3 A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution.
  2. The larger
    59_number The larger of two numbers is nine more than four times the smaller number. The sum of the two numbers is fifty-nine. Find the two numbers.
  3. Three sides
    triangle_vysky_2 Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
  4. Pool
    pool If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
  5. Store
    pave One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
  6. Cuboid
    cuboid Cuboid with edge a=24 cm and body diagonal u=50 cm has volume V=17280 cm3. Calculate the length of the other edges.
  7. Right triangle Alef
    r_triangle The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
  8. Circle arc
    pizza Circle segment has a circumference of 41.89 m and 251.33 m2 area. Calculate the radius of the circle and size of central angle.
  9. Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  10. Right triangle
    righttriangle Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
  11. Gear
    ozubene_kolesa Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
  12. Motion
    cycling Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di
  13. Barrel of oil
    dieselbarrel Barrel of oil weighs 253 kg. When it mold 43% oil, weighed 159 kg. What is the mass of the empty barrel?
  14. R triangle
    right_triangle_1 Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
  15. Rectangle - sides ratio
    rectangle_2 Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
  16. Pedestrian up-down hill
    peak Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
  17. Medians
    medias_triangle Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
  18. The cyclist
    cyclist The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town.
  19. Workers
    two_workers Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days. If every worker was working alone, how many days took whole work for worker A and B?
  20. Tourists
    hiking From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?

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