# Grade - examples - page 187

1. Counting number
What is the smallest counting number divisible by 2,5,7,8 and 15?
2. Sugar production
From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?
3. Our house
Our house would paint four painters in 14 days. How long could it paint five painters? How long will it take if two other painters will come to help after 5 days?
4. Cuboid
The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
5. Birthday
Mother bought 21 desserts on the occasion of Mirka's birthday one tips was 9 CZK and the kremlin cost 12 CZK. For all desserts, she paid 213 CZK. How many kremlins and how many tips mums did buy?
6. Butter
At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain?
7. Cube edges
The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
8. Pendulum
Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
9. Diagonals
What x-gon has 54 diagonals?
10. Clock hands
The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day?
11. Regular triangular pyramid
Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
12. Average age
The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company?
13. Exponential equation
Determine the value of having y in the expression (3^y): (4^-1)=36.Y is a natural number greater than zero.
14. Pupil age
I am a pupil of the primary school, I spent 1/4 of my age on the exercise of parents with children, 1/3 on drawing, 1/6 on flute. I did not have a ring for the first three years of my life and never went to two rings at once. How old am I?
15. Withdrawal
If I withdrew 2/5 of my total savings and spent 7/10 of that amount. What fraction do I have in left in my savings?
16. The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r
17. Train and walker
Walker passes an hour 5 km. Express train per hour 100 km. Walker went 4 hours. How many minutes took the distance express train?
18. Bicycle gear
The pedal bicycle wheel has 56 teeth and a rear 20 gear tooth. How many times does the bicycle wheel turn when you make 20 turns of the pedal wheel?
19. Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
20. Rainfall
A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.

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