# Examples for 9th grade - page 84

1. Storm So far, a storm has traveled 35 miles in 1/2 hour in direction straight to observer. If it is currently 5:00 p. m. and the storm is 105 miles away from you, at what time will the storm reach you? Explain how you solved the problem.
2. Bakery and flour The bakery tray for flour was filled to 3/4 volume. After removing 875 kg of flour, it was filled to only 2/5 of the volume. How many tons of flour is in the full tray?
3. The rope A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners?
4. Classroom There are eighty more girls in the class than boys. Boys are 40 percent and girls are 60 percent. How many are boys and how many girls?
5. Mother and daughter The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
6. Folded square ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
7. Hexagon cut pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
8. Big number hat is the remainder when dividing number 10 to 47 - 111 by number 9?
9. Magic number The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
10. Iron collecting Class 7A collected 3.2 tonnes of iron more than class 7B. Together they collected 6.4 tonnes of iron to the secondary raw material collection. How much did each class collect?
11. Diagonals A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
12. Diagonal he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
13. Area of iso-trap Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
14. Surface of cubes Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
15. Points on line segment Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
16. Remainder A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
17. Mushrooms Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
18. Embankment Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
19. Trapezoid - intersection of diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
20. Candy Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have?

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