Final answer:
The ratio of how Jarek, Jerzy, and Justyn share the chocolate bar is 5:3:2. Using this ratio, and given that Justyn is 8 years old, we can calculate that Jarek, who receives 5 parts of this ratio, is 20 years old.
Step-by-step explanation:
To determine how three brothers, Jarek, Jerzy, and Justyn, share a block of chocolate based on the provided ratios, we first identify that Jarek receives half of the block. If we consider the whole block as 1, this means Jarek gets 1/2. Jerzy then gets 3/5 of what is left (1/2). The remainder of the bar is 1 - 1/2 = 1/2, so Jerzy gets 3/5 of 1/2. Lastly, Justyn will receive the rest of the bar that is left after Jerzy's portion.
Calculating Jerzy's share: (3/5) * (1/2) = 3/10 of the bar.
Justyn's share is the remaining chocolate: 1 - 1/2 - 3/10 = 1/5 of the bar.
The ratio of the chocolate bar shared between Jarek:Jerzy:Justyn is therefore 1/2 : 3/10 : 1/5, which simplifies to 5 : 3 : 2 when we make the denominators the same (by finding the common denominator of 10).
To calculate Jarek's age based on Justyn's age of 8 and their sharing ratio of 5 : 3 : 2, we can set up a proportion. Since Justyn's age corresponds to 2 parts of the ratio, and he is 8 years old, 1 part of the ratio is 8 / 2 = 4 years. Therefore, Jarek's age corresponds to 5 parts, so he is 5 * 4 = 20 years old.