# Algebra - examples

1. Former price
The price of an article is cut by 10℅, to restore it to the former value, by what percent the new price must be increased?
2. Diamond and diagonals
A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
3. Pupils
There are 27 pupils in the classroom. They can swim 21 and ski nine pupils. Neither swim nor ski three pupils. How many pupils can swim and ski?
4. Dog price
Tereza agreed to get a dog and 6000 crowns a year for help in a dachshund breeding station. After eight months she had to finish work and got a dog and 2000 crowns. What price does a dog have?
5. Castle tower
The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.
6. Probability of intersection
Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?
7. Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
8. The diagram 2
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza and 45 for Petra. How long will take make records if they will work together?
10. The difference
The difference of two numbers is 1375. If their exact quotient is 12. Find the two numbers
11. Iron pole
The iron pole is in the ground 2/5 of its length, partly above the ground 1/3 is yellow, and the unpainted section is 6 m long. How long is the entire column?
12. Loan 5
Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out the loan? C
13. Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
14. Last page
Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
15. Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
16. Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit
17. Shopping center
The shopping center buys from the manufacturer bikes at a purchase price of 180 €. It sells them for a sale price of 250 €. However, in the advertising for the sale of these goods, the shopping center spent 20% of the selling price of all bicycles in stock
18. Potatoes
For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
19. Nine books
Nine books are to be bought by a student. Art books cost \$6.00 each and biology books cost \$6.50 each . If the total amount spent was \$56.00, how many of each book was bought?
20. Sand castle
Tim and Tom built a sand castle and embellished it with a flag. Half the pole with the flag plunged into the castle. The highest point of the pole was 80 cm above the ground, its lowest point 20 cm above the ground. How high was the sand castle?

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