# Equation - 9th grade (14y) - examples

1. RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
2. Six workers
Six workers planned to repair the roof in 5 days. After two days, two workers get sick. How long will the remaining workers complete the roof at the same rate of work?
3. Four painters
The company sent four painters to paint the school. They should be done in 12 days. After three days, one painter got ill. How long will the remaining painters paint the school?
4. Carla
Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter’s age was twice the sum of Carla’s and Jim’s age. Find the present age of each one of them.
5. Former price
The price of an article is cut by 10℅, to restore it to the former value, by what percent the new price must be increased?
6. Dog price
Tereza agreed to get a dog and 6000 crowns a year for help in a dachshund breeding station. After eight months she had to finish work and got a dog and 2000 crowns. What price does a dog have?
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza and 45 for Petra. How long will take make records if they will work together?
8. 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.
9. Garden
Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
10. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
11. Bonus
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
12. Right Δ
A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
13. Troops
Route is long 147 km and the first day first regiment went at an average speed 12 km/h and journey back 21 km/h. The second day went second regiment same route at an average speed 22 km/h there and back. Which regiment will take route longer?
14. 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?
15. 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?
16. Store
One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
17. Clock
How many times a day hands on a clock overlap?
18. Server
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
19. Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
20. 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.

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