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Practical exercises
{{exercise_number}}. Farmer John was growing potato in his garden. He put the grown potatoes into \latex{ 22 } sacks so that every sack contained the same weight of potato, then he started selling at the market. On the first day he sold \latex{ 9 } sacks and \latex{ 44 } \latex{ kg } of potato. On the second day he sold \latex{ 13 } \latex{ kg } less than 7 sacks of potato, and finally on the third day he sold \latex{ 6 } \latex{ kg } less than \latex{ 5 } sacks of potato. Thus he was left with half a sack of potato.
- How many \latex{ kg } of potato were in one sack?
- How much money did he get in total if he sold a kilogram for \latex{ 60 } Euro cents?
- How much profit did he make if \latex{ 60 }% of his income was his cost?
{{exercise_number}}. \latex{ 25 }% of the price of a dress is the profit of a tradesman. If he raised its price by \latex{ 10 } EUR, then one third of the price would be his profit.
- What is the price of the dress?
- How much shall he raise the price of the dress by so that he will have \latex{ 50 }% profit?
{{exercise_number}}. A \latex{ 4.8 } \latex{ m } wide and \latex{ 3 } \latex{ m } high mosaic picture is made of \latex{ 1,000 } pieces of square-shaped mosaic tiles. How many rows and how many columns does this picture have?
{{exercise_number}}. A company is about to launch three different types of product. The preliminary surveys show that if the first product is successful, then they will get double of the money invested in it, if the second one is successful, then they will get four times the money invested in it, and if the third one is successful, then they will get eight times the money invested in it. We also know that only one of the products is expected to be successful. How much money should be invested in each product, if the management of the company definitely wants to achieve \latex{ 1 } EUR profit per product, no matter which of the products becomes successful?
{{exercise_number}}. Cissy observed that the kitties really like the food meant for them if it is mixed from two types. One kilogram of the one that tastes like fish is \latex{ 10 } EUR, while one kilogram of the one that tastes like chicken is \latex{ 15 } EUR. In the shop selling pet food it is possible to mix the different types as the customers like.
- In what ratio are these mixed if the mixture costs \latex{ 14.3 } EUR, and if the shop charges \latex{ 10 }% extra compared to the prices of the original food?
- What is the net price of the food if \latex{ 27 }% VAT is charged for the sold product?
{{exercise_number}}. On a given day at the stock exchange the price of one MOL and one OTP stock cost exactly \latex{ 200 } EUR in total. When buying \latex{ 6 } MOL stocks and \latex{ 7 } OTP stocks and calculating with \latex{ 6 } EUR commission we have to pay \latex{ 1,256 } EUR.
- What is the price of the stocks separately?
- After a month the price of the OTP stocks increased by \latex{ 20 }%, while the price of the MOL stocks stayed the same. What would be our profit if we sold all the stocks and we again had to pay \latex{ 6 } EUR commission for selling?
- Would there be any profit if the price of the MOL stocks increased by \latex{ 20 }% and the price of the OTP stocks decreased by \latex{ 20 }%? The commission is \latex{ 6 } EUR for selling again.
- In the case of what percentage of increase would our profit be \latex{ 200 } EUR when selling all the stocks, if calculating with the same percentage of increase in the price of both of the stocks?
{{exercise_number}}. The Smith family pays a flat rate for water consumption, i.e. each month they pay the price of \latex{ 10 } \latex{ m^3 } of water irrespectively of their consumption. They found it expensive, therefore they decided to get a meter set up, which measures the actual consumption, and that they would pay according to this in the future. Setting up the meter cost \latex{ 100 } EUR. Considering the consumption of the first three months they experienced that their consumption was \latex{ 24 } \latex{ m^3 } over this period.
- In how many months does the setting up of the meter return if the price of \latex{ 1 } \latex{ m^3 } of water is \latex{ 7 } EUR?
- At what actual consumption would the cost of the meter return in one year?
{{exercise_number}}. The area on Earth which is needed to satisfy the energy and food demand of one person is called the “ecological footprint”. Today it is resulting \latex{ 1.8 } hectares when calculated with the average. In accordance with it the people, depending in which country and in what circumstances they live, use the earthly possessions to an extent different from the average. The ecological footprint of someone living in Hungary on the average is half as of someone living in Finland, whereas it is seven times as of someone living in Bangladesh. When considering these three countries \latex{ 6/7 } hectares would be resulting as average.
What is the size of the ecological footprint of someone living in Hungary if there are sixteen times as many people in Bangladesh and half as many people in Finland as in Hungary?
{{exercise_number}}. The purity of gold alloy is measured in carats. The carat shows how many twenty-fourth of the alloy is gold. For example if a gold alloy is \latex{ 17 }-carat, then \latex{ 17/24 } of it is gold, and the rest of it are distinct alloying additions. A jeweller would like to create a \latex{ 60-gram } \latex{ 20- }carat necklace, for which he can use \latex{ 17- } and \latex{ 22- }carat gold.
- What amount of gold should he use from each type to create the necklace?
- The jeweller could buy one gram of \latex{ 17- }carat gold for \latex{ 75 } EUR, and buy one gram of \latex{ 22- } carat gold for \latex{ 100 } EUR. For how much should he sell the necklace if he wanted to get \latex{ 25 }% profit?
{{exercise_number}}. We would like to save money. For this reason we deposit a definite amount of money in the bank at the beginning of each year for which the bank pays an annual interest rate of \latex{ 5 }%. What amount shall we deposit annually if at the end of the third year we would like to buy fitness equipment for \latex{ 331 } EUR?
{{exercise_number}}. A plant producing electric motors experimented with two types of motors, and it was examining how many kilometres the cars can travel with one charge. At the beginning the first motor could cover twice the distance as the second one. Two consecutive changes were implemented on each motor type. As a result the first motor could cover \latex{ 28 } \latex{ km } less each time, while the second one could cover \latex{ 20 }% more each time, and thus finally both of the motors could cover the same distance. What distance could they cover at the beginning?
