# Algebra - problems - page 69

Grandfather gathered apples into baskets. He filled one large and three small baskets. Small baskets are identical and each can hold 3 kg of apples less than in a large basket. In small baskets together 3 kg of apples over a large basket. How many kilogram
2. Paper squares
The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
3. VAT on books
The cost of a book in the store is 12.5 euros. How much euros is the VAT of this book? VAT is 10%.
4. Sides of triangle
Triangle has circumference 42 cm. Side a is 2 times shorter than side b and sice c is 2 cm longer than side a. Determine the sizes of sides of a triangle.
5. Variance and average
Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx).
6. Isosceles trapezoid
Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
7. Workers
9 workers dig a canal 120 meters long for eight hours. For how long would be dig five workers canal 200 meters long?
8. Contract
8 employees complete the contract for 65 hours. After 17 hours, 3 employees had to leave for another job. How many more hours will the job on contract be fulfilled?
9. Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this.
10. Candies
The price for 1 kg of more expensive candies is 125 CZK. The price for 1 kg of cheaper candy is 100 CZK. We mix two different mixtures of candy. A) The first mixture contains 2 kg more expensive and 0.5 kg cheaper candy. Calculate the price for 1 kg of t
11. Alcohol mixture
Three liters of 96 percent alcohol we set up a certain amount of distilled water to form a 54-percent alcohol. How many liters of distilled water were used?
12. Price saleoff
Shoes standing y euros. At first they were discounted by 12% and then 50% of the new amount. After this double cheapening the cost was exactly 22 euros. Determine the original price of shoes.
13. Water colors
Painting workshop attend 10 students. Eight students painted water colors and nine painted with tempera colors. How many students painted water colors and tempera at the same time?
14. Tailor master
There are less than 50m of textile in the tailoring workshop. When cutting on a blouse (consumption 1.5m), no textile is left. When using a cloth (consumption of 3.2m), no textile is left. How many meters of textile are in a tailor's workshop?
15. Two trains
There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
17. Unknown amount of money
Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis.
18. Comparing salaries
Spouses compared salaries. Mrs. Janka found that a 20% higher salary than Mr Jaroslav. Together earned € 1,430. How much they earn each of them?
19. Italian writer
There were 17 children in the barracks with an Italian writer. 6 children ordered a book in an Italian original and 12 children in the translation. How many children ordered a book in both languages if the three children did not order it?
20. Unknown number
Determine the unknown number, which double of its fourth square is equal the fifth its square.

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