# Natural numbers + system of equations - examples

1. Coins
The boy collected coins with value 5 CZK and 2 CZK when he had 50 pieces saved 190 CZK. How many he has each type of coin?
2. Euler problem
Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
3. Elections
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?
4. Sequence
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
5. Crown
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?
6. Chicken
I threw three chicken for a handful of grains and I noticed that it eat in a ratio of 8:7:6 and two of them grabbed 156 grains. How many grains have fought that chicken?
7. Tickets
Tickets to the zoo cost \$4 for children, \$5 for teenagers and \$6 for adults. In the high season, 1200 people come to the zoo every day. On a certain day, the total revenue at the zoo was \$5300. For every 3 teenagers, 8 children went to the zoo. How many te
8. Landlord
Landlord had 49 ducats more than Jurošík. How many ducats Jurošík steal landlord if the Jurošík now 5 ducats more?
9. Product
The sum and the product of three integers is 6. Write largest of them.
10. CZK coins
Thaddeus and Jolana together have 15 CZK. Jolana has half of Thaddeus money. Nevertheless Jolana has 3 coins and Thaddeus 2 coins. Which coin has Thaddeus and Jolana (Help: CZK coins has values 1,2,5,10,20,50 CZK)?
11. Algebrogram
Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
12. 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?
13. Balls
Michal said to Martin: give me one ball and I'll have twice as you. Martin said: give me 4 and we will have equally. How many balls each have?
14. Algebrogram
Solve algebrogram: mama+anna=vari How many solutions are?
15. Odd numbers
The sum of four consecutive odd numbers is 1048. Find those numbers ...
16. Unknown number 10
Number first increased by 30%, then by 1/5. What percentage we've increased the original number?
17. Sales of products
For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
18. Four integers
Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
19. MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
20. Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.

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