# Algebra - problems - page 67

1. Land areas
Two land areas is 244 m2. The first parcel is 40 m2 less than twice of the second one. What have acreage of each parcel?
2. Rectangle
Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.
3. Unknown number 4
I think number. When I divided its square root by its 1/9, I get a number 1. What number am I thinking?
4. Rectangle
The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
5. Trench
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
6. Sale off
Product cost 95 euros before sale off. After sale off cost 74 euros and 10 cents. About what percentage of produt became cheaper?
7. Tiles
It is given an area of 5m x 4m One tile is 40 x 40 cm How many tiles are needed in an area of 5 m x 4 m? And how many tiles need to be cut (if it not possible for the tiles to fall exactly)?
8. Body diagonal
The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
9. The pool
The pool has a volume of 40 m3 and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
10. Money
Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael.
11. 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.
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
13. 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%.
14. 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).
15. 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.
16. 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.