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Answer :
Final answer:
The total prize money is determined by first finding the value of one part of the distributed ratio, which is £125, by dividing the given difference (£250) by 2. The total prize money is then calculated by multiplying the value of one part by the total parts in the ratio, which in this case is 4, resulting to £500.
Explanation:
This problem deals with the mathematical concept of ratio distribution. When a quantity is shared in a specific ratio, it means the amount that parts receive are proportional to their size in the ratio. In this case, the prize money is shared between the winner and the runner up in the ratio 3:1.
This means the winner receives 3 parts of the prize, and the runner up receives 1 part. The difference between what they get is 2 parts (3 - 1 = 2), and this is given as £250. So, one part of the prize is worth £125 (£250 ÷ 2).
Since the whole prize is made up of 4 parts (3 parts for the winner and 1 part for the runner up), you would calculate the amount of the total prize by multiplying the value of one part by 4. Hence, the total prize money is £500 (£125 x 4).
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Answer:
£500
Step-by-step explanation:
ratio of money = 3 : 1 = 3x : x ( x is a multiplier )
winner receives £250 more than the runner up, that is
3x = x + 250 ( subtract x from both sides )
2x = 250 ( divide both sides by 2 )
x = 125
total prize money = 3x + x = 4x = 4 × 125 = £500
