# Examples for 9th grade - page 62

1. Three dice
When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
2. Heating plant
Workers dump imported coke at heating plant. On the first day used half of the amount, the second day three quarters the rest and on the third day left 120 tons. How much coke they dump at heating plant?
3. Book
Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
4. Percentage and rectangle
About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?
5. Debt
Joe and Caryl have a debt of \$100,500. Joe makes \$90,000 per year, and Caryl makes \$35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries?
6. Meat
Half a kilogram of pork and three-quarters of a kilogram of beef cost total 5.1 USD. One quarter of a kilogram of beef and 1 kilogram of pork cost 4.9 USD. Determine the price of 1 kg of each type of meat.
7. Shoes and slippers
Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers?
8. Chord distance
The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm.
9. The city
At the end of 2010 the city had 248000 residents. The population increased by 2.5% each year. What is the population at the end of 2013?
10. Water reservoir
The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
11. Trapezoid v3
The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ?
12. Diamond
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
13. Rain
How many mm of water rained the roof space 75 m2 if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-)
14. Mortgage
Family XY wants to take the bank mortgage (loan for an apartment/house) in the amount of € 100,000. Bank for processing the mortgage charges a fee of 0.79% of the amount borrowed. How many euros is this fee?
15. Coins
In ticket maschine were together one hundred coins. They were only 20 and 50 cent coins. The sum total was 29 euros and 60 cents. How many were in ticket maschine coins and which type?
16. Cone area and side
Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
17. Sweets
3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations
18. Car and cyclist
Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car?
19. Equilateral triangle v3
Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle.
20. Parcel
parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel?

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