8th grade (13y) + system of equations - examples
- Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
solve equations by substitution: x+y= 11 y=5x-25
- Simple equations
Solve system of equations: 5x+3y=5 5x+7y=25
- Mother and daughter
The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
- Iron collecting
Class 7A collected 3.2 tonnes of iron more than class 7B. Together they collected 6.4 tonnes of iron to the secondary raw material collection. How much did each class collect?
- Boys and girls
There are 48 children in the sports club, boys are 10 more than girls. How many girls go to the club?
If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately?
- Forestry workers
In the forest is employed 63 laborers planting trees in nurseries. For 11 hour work day would end job in 43 days. After 14 days, 22 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 15 hours
Mr. Radoslav calculated that excavation for a water connection dig for 10 days. His friend would take 7 days. Radoslav worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
One meter of the textile were discounted by 2.4 USD. Now 6 m of textile cost as before 3 m. Calculate the old and new price of 1 m of the textile.
If you go at speed 6.1 km/h, you come to the station 51 minutes after leaving train. If you go by bike to the station at speed 17 km/h, you come to the station 43 minutes before its departure. How far is the train station?
In stock are three kinds of branded coffee prices: I. kind......5.3 USD/kg II. kind......11.6 USD/kg III. kind.....5.8 USD/kg Mixing these three species in the ratio 2:8:3 create a mixture. What will be the price of 800 grams of this mixture?
- Right triangle Alef
The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
Cyclist started out of town at 20 km/h. After 0.6 hours car started behind him in the same direction and caught up with him for 52 minutes. How fast and how long went car from the city to caught cyclist?
- Chickens and rabbits
In the yard were chickens and rabbits. They had 44 heads and 124 legs. How many chickens and how many rabbits was in the yard?
- Circle arc
Circle segment has a circumference of 13.26 mm and 252.03 mm2 area. Calculate the radius of the circle and size of central angle.
- Triangle ABC
Calculate the sides of triangle ABC with area 883 cm2 and if a: b: c = 15:7:19
- Right triangle
Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle.
Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D
Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?