# Examples for 9th grade - page 102

1. Three numbers We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
2. A man 2 A man divides \$10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
3. Luggage and air travel Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lugg
4. KLM triangle Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
5. Ruler and compass Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
6. Three brothers The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them? The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste? The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
9. Six workers Six workers planned to repair the roof in 5 days. After two days, two workers get sick. How long will the remaining workers complete the roof at the same rate of work?
10. Employees There are 1116 people working in three factory halls. In the first one, there are 18% more than the third, and 60 persons more than the second. How many employees work in individual halls?
11. Bricklayer How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420?
12. Girls The children's competition was attended by 63 girls, which is 30% of all children's participants. How many children attended this competition?
13. A boy A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
14. Paratrooper After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land fr
15. Ratio of sides Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
16. Coins The boy collected coins with value 5 CZK and 2 CZK when he had 50 pieces saved 190 CZK. How many he has each type of coin?
17. Test scores Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?
18. T-shirts and hat 5 t-shirts and a hat cost £62.00 2 t-shirts and a hat cost £29.00 How much does a t-shirt cost ? How much does a hat cost ?
19. Tangent spheres A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and
20. Isosceles triangle In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?

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