# System of equations - examples - page 12

1. Parabola
Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
2. Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
3. Legs
In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
4. Cars speeds
Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
5. Cargo
Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load?
6. Three workers
Three workers were rewarded CZK 9200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received?
7. Eva
When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet?
8. Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
9. Rectangular field
One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.
10. Have solution
The sum of four consecutive even numbers is 96. Determine these numbers.
11. Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
12. The city
In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
13. Diamond diagonals
Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
14. James
James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
15. Purchase
Three buyers pay € 468. The first paid 3-times more than second, third half over second. How many euros paid each of them?
16. Null points
Calculate the roots of the equation: ?
17. Mother and daughter 2
The mother is 40 years older than her daughter. How old is the mother if her age is eight thirds age of daughter?
18. Crates 2
In 6 crates is 45 kg of apples In  5 crates is equally In 1 in crate is 3 kg more How many kilograms in each crate?
19. Stamps and albums
Michail has in three albums stored 170 stamps. In the first album, there are 14 more than in the second and in the second is by 1/5 less than in the third. How many stamps are in the first album?
20. Football season
Throughout the football season gave Adam the 23 goals more than Brano and 16 goals less than Karol. Edo gave the 6 goals more Dušan. Karol gave 5 more than Edo. Brano and Edo gave together 17 goals. How many goals gave each boy and how many goals gave the.

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