System of equations - examples - page 5
- Newton's task
Grass grows in the meadow equally fast and evenly. It is known that 99 cows graze meadow for 14 days and 95 cows by 22 days. How many cows graze meadow for 77 days?
Lawyer got to pay 840 Euros in banknotes of 20 and 50 Eur. Total got 18 banknotes. How many was which?
At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 4 L of 48-percent solution. What amount of solution from each container is needed to mix?
- Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
- Father and son
Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son?
- Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=60°. What sizes have other angles in a triangle?
- Two valves
Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days. How many days took to fill the pool each of the valves individually?
- Ladislav in Amsterdam
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books?
The elections attended a total 4818 voters. First day 39 men more than women, the second day 21 women more than men. How many women attended elections?
- Forth and back
Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
The perimeter of the parallelogram is 117 cm. The length of one side is 1.9-times longer than the length of the shorter side. What is the length of sides of a parallelogram?
- Metal alloy
What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When grand
The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla
Figliarko has 13 cents less than Hana. Together they have 57 cents. How many cents has Hana and how many Figliarko?
- Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
- Honza + Alice + Tonda
Honza + Alice + Tonda have a total of 111 USD. The ratio between Honza and Alena is 5:6 and the ratio between Alice and Tonda is 4:5 How many money have each of them?
- Cross-country competition
Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B?
Siblings collect a 2-crowns and 5-crowns. Together have 80 coins with a total of value 310 crowns. How many saved two-crowns and how many five-crowns?
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