# 5th grade (10y) + system of equations - examples

1. Two squares
Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.
2. Chamber
In the chamber light is broken and all from it must be taken at random. Socks have four different colors. If you want to be sure of pulling at least two white socks, we have to bring them out 28 from the chamber. In order to have such certainty for the pai
3. Cents
Julka has 3 cents more than Hugo. Together they have 27 cents. How many cents has Julka and how many Hugo?
4. Lentilka
Lentilka made 31 pancakes. 8 don't fill with anything, 14 pancakes filled with strawberry jam, 16 filled with cream cheese. a) How many Lentilka did strawberry-cream cheese pancakes? Maksik ate 4 of strawberry-cream cheese and all pure strawberry pancake
5. Rabbits
In the hutch are 48 mottled rabbits. Brown are 23 less than mottled and white are 8-times less than mottled. How many rabbits are in the hutch?
6. Trio
Trio of workers earn 750 euros. Money divided by the work that each of them made​​. First received twice as the second, the second received three times more than the third. How many got everyone from workers?
7. Father and son
Father and son are together 80 years. Son is 28 years younger than father. How old is the son?
8. Gardens
The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
9. Family
Martin has just as brothers as sisters. His sister Jana but has 2 times more brothers than sisters. a) How many children are in this family? b) How many boys and how many girls are in the family?
10. Warehouses
To four warehouses is going cement in 25 kg bags. To first one third, to second quarter of the total. The third store got two thirds of the rest, and the last 310 tons came to fourth. How many cement is in all warehouses and how much got every one?
11. 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?
12. Chestnuts
Neil has 5-times chestnuts less than Adrian. Together they have 894 chestnuts. How many chestnuts has Neil and Adrian?
13. Landlord
Landlord had 49 ducats more than Jurošík. How many ducats Jurošík steal landlord if the Jurošík now 5 ducats more?
14. Bob and Bobek
Bobek has 2 cabbages and 5 carrots, Bob has 2 cabbages and 9 carrots. When Bobek stepped on the scale weight 5800 g and when Bob weight 8960 g. Actual Bob weight is 8 kg and Bobek 5 kg. How much weighs one carrot?
15. ZOO
In the zoo was elephants as many as ostrichs. Monkeys was 4 times more than elephants. Monkeys were as many as flamingos. Wolves were 5 times less as flamingos. How many of these animals were together? We know that there were four wolves.
16. Shoes
Peter decided to measure shoes size of his three friends. Measured accurately and wrote as follows: Venda and Jenda together 52 cm Jenda and Zdenda together 58 cm Zdenda and Venda together 54 cm a) How long measures Vendy, Jenda and Zdenda shoes together
17. Rabbit family
Rabbit family ate 32 pieces of carrots, small one ate 6 pieces, dad 5 more than the mother. How much ate mom?
18. Triangle ABC
In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm.
19. Birds
On the farm they have a total of 110 birds. Geese and turkeys together is 47. Hens is three times more than the turkey. How much is poultry by species?
20. Toys
The toy shop sold the same number of balls for 62 CZK and skipping ropes for 34 CZK. They income was 576 CZK. How many sold balls and how many skipping ropes?

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