# Grade - math word problems

1. Monty Hall Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.
2. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
3. Two boats Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
4. Prism The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
5. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?
6. Distance Calculate distance between two points X[18; 19] and W[20; 3].
7. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
8. Count of triangles Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
9. Sequence Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
10. Fraction Determine for what x fraction ?:
11. Null points Calculate the roots of the equation: ?
12. School trip School trip cost 247.2 Eur for one class (24 students). How much would cost a trip for two classes? (both classes together have 53 students)
13. Logic A man can drink a barrel of water for 26 days, woman for 48 days. How many days will a barrel last between them?
14. Triangle and its heights Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
15. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
16. Negative percentage In 2004, the company had a loss of 40900 Euros. Two years later he was already in profit 48900 Eur. Calculate what percentage of the company increased profits in this two years.
17. RBA Regional Building Authority has an annual budget of EUR 1806814. In previous calendar year has processed 804 approval procedures. How much does an average of one building approval costs (eg unsuccessful revoke)?
18. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
19. Quarter circular The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
20. Homework The monthly fee for the phone is 12 USD and for phone unit 0.08 USD. How much family pay phone in the first quarter Q1, if on January 1 had on the counter 97362 units and on April 1 97946 units.

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