System of equations + reason - math problems
Number of problems found: 208
- Apple collecting
Luke, Peter and Tibor compared how many kilograms of apples they had collected. They found that the arithmetic mean of what Luke and Peter collected was 10 kg larger than Tibor's contribution, and the arithmetic mean of what Luke and Tibor collected was 3
- Two numbers
One number is by 79 larger than the other. If we divide the larger number by the smaller one, we get the ratio 5 and the remainder 11. Determine both numbers.
- In the library
In the library at Lenape Elementary School, there are 2/5 as many fiction books as there are nonfiction books. There are 56 books in the school library. How many books are fiction books?
- Maria 2
Maria is 7 years older than her brother Robert and in 2 years her age will be four times what Robert’s age was three years ago. Find their present ages.
- Fruit equation
Find how many peaches could be bought instead of buying one melon, one pear, one apple and two plums if we know that: • Melon and plum cost the same as three apples • if we subtract the price of a pear from the price of peach, we get the price of plum • T
- Two workers
One worker makes a part 4 hours and the second 9 hours later than they would make the same part together. How long does it take for each worker to make the part himself?
- Two-digit number
In a two-digit number, the number of tens is three greater than the number of units. If we multiply the original number by a number written in the same digits but in reverse order, we get product 3 478. Find the original number.
- THE FARM
Hens, goats, and 3 cows grow on the farm. All animals have a total of 19 heads and 56 legs. How many goats live on the farm, and how many hens live on the farm?
Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length, their longer sides are three consecutive natural numbers. Fi
- The difference 2
The difference between the two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number?
A buyer said, "I want to buy 100 pigs for 100 denarii. An adult pig costs 10 denarii, a sow 5 denarii, two little piglets are worth 1 denarius. " How many pigs, sows and piglets could he buy for exactly 100 denarii?
Tourists hire a guide. Everyone will pay the same amount. If there are two less of them, they will pay 14 crowns more, and if there are three more, they will pay 14 crowns less. How many tourists are there and how much have the guides paid.
- The family
How old is a mother if she is four times older than her daughter and 5 years ago she was even seven times older than her daughter? Today, a son is 30 years younger than a father. 7 years ago, a father was seven times older than a son. How old is a son tod
- Two grandmothers
Two grandmothers went to sell eggs at the market, and they had a total of 100. When they sold all the eggs, they made the same money. The first grandmother says to the second: "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmot
- Coloured numbers
Mussel wrote four different natural numbers with coloured markers: red, blue, green and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div
- Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice
The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.
- Father and son
When I was eight years old, my father was 30 years old. Today, my father is three times more than me. How old am I?
- Lottery - eurocents
Tereza bets in the lottery and finally wins. She went to the booth to have the prize paid out. An elderly gentleman standing next to him wants to buy a newspaper, but he is missing five cents. Tereza is in a generous mood after the win, so she gives the m
Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo
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