# Examples for 9th grade - page 80

1. Trapezoid - central median The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
2. Acres Two hours 24 students harvested chestnuts on 36 acres. How many square meters harvested one student per hour?
3. Prize How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?
4. Ravens On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree?
5. Cross section The cross-section ABCD of a swimming pool is a trapezium. Its width AB=14 meters, depth at the shallow end is 1.5 meters and at the deep end is 8 meter. Find the area of the cross-section.
6. Fifth member Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
7. Rectangle 35 Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
8. The rectangle Determine the area of the rectangle where the length and width are in the ratio 5:2 and its length is 7.5 cm longer than its width. Determine also its length and its width.
9. Unknown number x 5% from an unknown number equals the number 26. What is the unknown number?
10. Pond A pond with two open floodgates will emptied in 20 days. A larger floodgate will emptied whole pond in 30 days. For how long would he be emptied with a smaller floodgate.
11. Apples Apples I picked 600 kg this year. Autumn's apples was 4 times more than the summer. How many kg's I picked the summer and how much winter apples?
12. Walnuts x walnuts were in the mission. Dano took 1/4 of nuts Michael took 1/8 from the rest and John took 34 nuts. It stayed here 29 nuts. Determine the original number of nuts. On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
14. One percent One percent of all the lights in the city are LED, the remaining 99% are conventional. Other types are not there. John counted them honestly but he had counted only conventional. After a good dinner he registered numbers and he have notice that from all t
15. Boys and money 270 USD boys divided so that Peter got three times more than Paul and Ivan has 120 USD more than than Paul. How much each received?
16. Regular n-gon In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
17. Two aircraft From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour.
18. Arithmetic progression In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ?
19. Socks One pair of socks worth CZK 27. Set of 3 pairs of these socks are sold with 10% discount. How many we will pay CZK for two offered sets of socks?
20. Tricolors From the colors - red, blue, green, black and white, create all possible tricolors.

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