# Algebra - math word problems

1. Parallelogram Rhomboid (parallelogram) has a longer side of 50 cm long. The size of its one height is four times the size of its second height. Calculate the length of the shorter side of this rhomboid in the centimeters.
2. Banknotes Eva deposit 7800 USD in 50 banknotes in the bank. They had value 100 USD and 200 USD. How many were they?
3. Reminder and quotient There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
4. Father and son Father and son weigh together 108kg. The father weighs 2.6 times more than his son. How much does weight my father and son count?
5. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
6. Cows and calves There are 168 cows and calves in the cowshed. Cows are in nine stalls and calves in four stalls. Same count cows are in every cow stall and three more in each calf stall than in a cow stall. What is the capacity of the stalls for cows and what for calves?
7. Hyperbola equation Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
8. Curve and line The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
9. Equations - simple Solve system of linear equations: x-2y=6 3x+2y=4 A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
11. 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
12. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
13. Train speed Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:
14. Rectangular garden 2 A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
15. Supplementary angles One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
16. Non linear eqs Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
17. Poplar How tall is a poplar by the river, if we know that 1/5 of its total height is a trunk, 1/10th of the height is the root and 35m from the trunk to the top of the poplar?
18. The length The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
19. Evaluation of expressions If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
20. Three workshops There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?

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