Equation - high school - math problems

1. Age problems A) Alex is 3 times as old as he was 2 years ago. How old is he now? b) Casey was twice as old as his sister 3 years ago. Now he is 5 years older than his sister. How old is Casey? c) Jessica is 4 years younger than Jennifer now. In 10 years, Jessica wi
2. Camel and water 84% of the camel's weight is water. After drinking, its weight increased to 832 kg and water accounted for 85% of its weight. How much did it weigh before drinking?
3. Geometric progressiob If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
4. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
5. Prices The price of the product was increased by 35%. How many percents of the new price we have to make it cheaper so that its price is equal to the original price?
6. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
7. Pool If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
8. Bonus Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
9. 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?
10. Beer After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
11. Clock How many times a day hands on a clock overlap?
12. Server Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
13. Discount Ladies sweater was twice discounted. First by 11%, then by 11% of the new price. Its final price was 100 €. Determine the original price of sweater.
14. River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
15. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
16. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
17. 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?
18. Two cars Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?
19. Circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
20. Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18

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