System of equations - 6th grade (11y) - math problems

  1. The fruit basket
    jablka The fruit basket is five times heavier than the empty basket. Filled is 20kg heavier than empty. Determine the weight of the fruit in the basket.
  2. Dividing money
    mince_2 Vilem, Cenek, and Edita divided the money they earned by spreading the leaflet. Vilem got 240 CZK more than Cenek and twice more than Edita. Edita got 400kc less than Vilem.
  3. Square into three rectangles
    stvorcove-cisla_1 Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
  4. Buns and toasts
    vaha_16 Two buns weigh 10 grams more than two toasts. One Bun and two Toast weigh a total of 110 grams. How many grams weigh three toasts? How many grams does a Bun weigh?
  5. The tourist
    cyclist_28 The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
  6. Wine
    vino_1 A bottle of wine costs 21 euros; and wine is 20 times more expensive than a bottle. How much a bottle cost?
  7. Guess a fraction
    fractions_1 Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form)
  8. Crown coins
    coins_1 Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
  9. Rectangle
    rectangle_4 The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?
  10. Have solution
    numbers_44 The sum of four consecutive even numbers is 96. Determine these numbers.
  11. Benches
    garden_13 The park has 64 benches. Occupied are by 18 more than empty. How many benches are occupied and empty ?
  12. Triangle ABC
    triangles_6 In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm.
  13. Pets in ZOO
    chicken_3 The zoo have run for pets. They are chickens, pigs and cow. Altogether there has 20 heads and 60 feet. How many chickens and piglets are there?
  14. Subjects
    math_series_1 Student makes a mathematical task for five minutes and the task from biology in twelve minutes. Another day he have homework in math and biology which consists of eleven tasks together. To do the job took hour and a half. How many tasks maked in each subj
  15. Family
    family_5 Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
  16. Bag
    taska Nelly found interesting point. An empty bag weighs 4 kg less than full. And empty bag is 5 times easier than full. How many kg weigh things in this bag?
  17. Rings groups
    venn 27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups?
  18. Can
    konev Watering can full of water weighs 10 kg. Half-full can weighs 5.5 kg. How much weigh can?
  19. Saving
    euro2 The boy has saved 50 coins € 5 and € 2. He saved € 190. How many were € 5 and how many € 2?
  20. Children
    weight_1 Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh?

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