To determine how much the first prize winner receives, we need to follow a step-by-step approach:
1. Understand the Ratio: The prize money is shared among three winners in the ratio 4:2:1. This means if the total prize money were divided into equal parts, the first winner would get 4 parts, the second winner would get 2 parts, and the third winner would get 1 part.
2. Calculate the Total Number of Parts: Sum the parts in the ratio:
[tex]\[
4 + 2 + 1 = 7
\][/tex]
So, the total prize money is divided into 7 equal parts.
3. Determine the Value of One Part: Divide the total prize money by the total number of parts:
[tex]\[
\frac{£3801}{7}
\][/tex]
Let's calculate this:
[tex]\[
\frac{3801}{7} = 543
\][/tex]
Each part is worth £543.
4. Determine the First Winner's Share: Since the first winner receives 4 parts:
[tex]\[
4 \times 543 = 2172
\][/tex]
So, the first prize winner receives £2172.
Therefore, the first prize winner receives £2172.
