Final answer:
To calculate the total prize shared in a ratio of 0.45:100, representing 45:10000 when simplified, we use the given difference of €178.50 between Cathy and Conor's received amounts. Solving for the value Conor received and adding Cathy's additional amount, the total prize value comes to approximately €357.81.
Step-by-step explanation:
To find the value of the prize shared between Cathy and Conor, we need to understand the given ratio and the amount that Cathy received more than Conor. The ratio given is 0.45:100, which can be simplified to 45:10000 by multiplying both parts by 100 to avoid decimals. Now, let's call the amount that Cathy received 'C' and the amount Conor received 'K'.
According to the ratio, for every 45 parts of the prize Cathy receives, Conor receives 10000 parts. Cathy received €178.50 more than Conor did, which can be represented by the equation C = K + €178.50. Plugging in the ratio values gives us 45K = 10000C. However, to solve for the prize value, it's easier to consider Conor's part to be 'x' and Cathy's part to be x + €178.50. The total prize is the sum of Conor's and Cathy's amounts, which gives us the equation:
Total Prize = Conor's amount + Cathy's amount = x + (x + 178.50)
By substituting the ratio, we get 45(x + €178.50) = 10000x.
Solving this equation:
- 45x + 8022.50 = 10000x
- 8022.50 = 10000x - 45x
- 8022.50 = 9955x
- x ≈ €0.806
The value of the prize that Conor received is €0.806. Since we know that Cicely got €178.50 more than this amount, her share is €179.306 (0.806 + 178.50). Thus, the total value of the prize is €179.306 (Conor's share) + €178.50 (the difference) = €357.806
Therefore, the total value of the prize is approximately €357.81 when rounded to the nearest cent.