# Examples for 9th grade - page 68

- Cuboid and ratio

Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm^{2}. Calculate the volume of the cuboid. - Ten dices

When you hit ten dices at the same time you get average 35. How much do you hit if every time you get six, you're throwing the dice again? - Consecutive numbers

Sum of ten consecutive numbers is 105. Determine these numbers (write first and last). - Unknown number 7

16% of the unknown number is by 21 less than unknown number itself. Determine the natural unknown number. - Students

In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row. - Sales of products

For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold? - Triangle angles

In a triangle ABC the interior angle at the vertex C is twice as the internal angle at the point A. Outer angle at the point B measured 117 degrees. How big is the outer angle at the vertex A? - Ski tow

The ski club has 168 pupils and used lift with 60 seats, while students always follow the same sequence in filling seats. How many times while riding a ski lift skier sitting in the same seat as the first run? - Parking

120 vehicles parking on the morning. Pasenger car is charged 20 CZK, 50 CZK per bus. The guard collected for parking 2640 CZK in total. How many cars and how many buses stood in the parking? - Mr and Mrs

Mr. Calda and Mrs. Cald have a total of 139 years. How many years have when we know that Mr. Calda is 9 years older than Mrs. Cald - Billboard

Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard. - Sales stores

The first sales store passed the 1/3 and the second 2/5 of the total amount of goods.In third store passed the 2/3 rest of the goods. The remaining 40 kg of goods put into fourth store. How many kilograms of goods pass to a third store? - Sum or product

What is the probability that two dice fall will have the sum 7 or product 12? - Pears

Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears. - Class pairs

In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula? - Hollow sphere

The volume of the hollow ball is 3432 cm^{3}. What is its internal radius when the wall thickness is 3 cm? - Sides ratio

Calculate the circumference of a triangle with area 84 cm^{2}if a:b:c = 10:17:21 - Dividing money

Thomas, Honza and Vasek are to divide 1220kč. Honza got 25% more than Thomas. Vasek 20% less than Thomas. How CZK each got? - Points on circle

In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are i - Apples 2

How many apples were originally on the tree, if the first day fell one third, the second day quarter of the rest and on tree remained 45 apples?

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