9th grade (14y) + system of equations - examples
- MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
- Two numbers 7
The sum of two consecutive even numbers is 30. Find the numbers.
- 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?
- The tourist
The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone?
- Linear system
Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2
- Two diggers
Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
- Tickets 4
Stacey is selling tickets to the school play. The tickets are $7 for adults and $5 for children. She sells twice as many adult tickets as children's tickets and brings in a total of $342. How many of each kind of ticket did she sell?
- Three brothers
The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
- TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
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.
Cuboid with edge a=24 cm and body diagonal u=50 cm has volume V=17280 cm3. Calculate the length of the other edges.
- Right triangle Alef
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
- Circle arc
Circle segment has a circumference of 41.89 m and 251.33 m2 area. Calculate the radius of the circle and size of central angle.
- Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
- Right triangle
Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
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
- 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?