Problem

Source: 2021 Swedish Mathematical Competition p2

Tags: number theory



Anna is out shopping for fruit. She observes that four oranges, three bananas and one lemon costs exactly the same as three oranges and two lemons (all prices are in whole kroner). Just then her friend Bengt calls, and Anna tells this to him. Bengt complains, that ''information is not enough for me to know how much each fruit costs''. ''No'', says Anna,' 'but three oranges and two lemons cost as many kroner as your mother is old''. Unfortunately, it's not enough either, but if she had been younger then the information would have been sufficient for you to be able to figure out what the fruits costs. How old is Bengt's mother?