# System of equations - examples - page 19

1. Geometric sequence 5
About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
2. Family parcels
In father will he divided the land so that the older son had three bigger part than younger son. Later elder son gave 2.5 ha field to younger and they had both the same. Determine the area of family parcel.
3. Two numbers
The sum of the two numbers is 1. Find both numbers if you know that half of the first is equal to one seventh of the second number.
4. Rabbits 3
Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?
5. Two numbers
We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
6. Glass
Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
7. Tickets
On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
8. Three numbers
What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
9. Bags
The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
10. AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
11. Family
Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
12. Angles in ratio
The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
13. Linear function
What is the equation of linear function passing through points: a) A (0,3), B (3,0) b) A (-2,-6), B (3,4)
14. Potatoes 6
The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes d
15. Remuneration
Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received?
16. Krkonose CZ
Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t
17. Pets in ZOO
The zoo have run for pets. They are chickens, pigs and cow. Altogether there has 20 heads and 60 feet. How many chickens and piglets are there?
18. Sum of three numbers
The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
19. Journey to school
On the way to school I went steady step. In the first half of the journey, I counted every second step, in the second half every third. How many steps I do when I went to school if I counted double step are 250 more than three steps?
20. Savings
Paul has a by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have 3 boys together?

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