# Algebra - math word problems

1. IS trapezoid Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
2. Cherries Cherries in the bowl can be divided equally among 19 or 13 or 28 children. How many is the minimum cherries in the bowl?
3. Theater The theater has in each row with 19 seats. Ticket to the first 10 rows is for 30 USD. In next rows is for 15 USD. The theater was completely sold out. Revenue was 12255 USD. How many rows are in the theater?
4. Right triangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
5. Spherical cap From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
6. Sea water Seawater contains about 4.3% salt. How many dm3 of distilled water we must pour into 5 dm3 of sea water to get water with 1.8% salt?
7. Camp In the camp are children. 1/2 went on a trip, 1/4 went to bathe and 38 children remained in the room. How many children are in camp?
8. Barrel of oil Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel?
9. Rectangle - sides ratio Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
10. Rhombus and inscribed circle It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
11. Car Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B?
12. Gear Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
13. Rectangle In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
14. Cone Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
15. Motion Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di
16. R triangle Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
17. When will I be a millionaire? Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures ignore.
18. Tangents To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. Convert 270° to radians. Write result as multiple of number π. Mixing 62 kg of sea water with 84 kg rainwater is created water containing 3.1% salt. How many percent sea water contains salt?