Natural numbers + system of equations - examples
- 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.
- 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?
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?
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
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?
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?
Landlord had 49 ducats more than Jurošík. How many ducats Jurošík steal landlord if the Jurošík now 5 ducats more?
The sum and the product of three integers is 6. Write largest of them.
- 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)?
Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
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?
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?
Solve algebrogram: mama+anna=vari How many solutions are?
- Odd numbers
The sum of four consecutive odd numbers is 1048. Find those numbers ...
- Unknown number 10
Number first increased by 30%, then by 1/5. What percentage we've increased the original number?
- 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?
- 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.
- Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
- Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
- Candy and boxes
We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of.