8th grade (13y) + system of equations - examples

  1. Value 4
    fractal_11 If 5/18=425 what is the value 13/18?
  2. The sides
    rectangle_9 The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
  3. Soaps
    mydlo_1 Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
  4. Two equations
    children_23 Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
  5. 12 apples
    apples_11 12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread?
  6. 13 tickets
    zamek_1 A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
  7. Perimeter of a rectangle
    rectangle_4 If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?
  8. 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?
  9. Forestry workers
    forestry_workers In the forest is employed 64 laborers planting trees in nurseries. For 8 hour work day would end job in 35 days. After 12 days, 20 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 9 hours a
  10. Excavation
    vykop_ryha Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
  11. 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.
  12. Motion
    cyclist_1 If you go at speed 5.1 km/h, you come to the station 37 minutes after leaving train. If you go by bike to the station at speed 28 km/h, you come to the station 38 minutes before its departure. How far is the train station?
  13. Coffee
    coffe In stock are three kinds of branded coffee prices: I. kind......6.9 USD/kg II. kind......8.1 USD/kg III. kind.....10 USD/kg Mixing these three species in the ratio 8:6:3 create a mixture. What will be the price of 1100 grams of this mixture?
  14. 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.
  15. Motion2
    car_cycle Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
  16. Chickens and rabbits
    pipky In the yard were chickens and rabbits. They had 31 heads and 94 legs. How many chickens and how many rabbits was in the yard?
  17. 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.
  18. Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  19. 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.
  20. 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

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