Final answer:
To find the total prize, the difference between the shares is used to determine one part of the ratio (5:1), which is £20. Multiplying this by the total ratio parts (6), the total prize is calculated to be £120.
Step-by-step explanation:
The student's question asks about dividing a prize in the ratio 5:1 and finding the total prize amount when the difference between the two shares is £80.
To calculate this, we assume that the smaller share (1 part of the ratio) is 'x' pounds.
Therefore, the larger share (5 parts of the ratio) will be '5x' pounds.
We know the difference between the larger and smaller share is £80, which gives us the equation '5x - x = 80'
'4x = 80'.
Solving this, we find that 'x = 20', meaning the smaller share is £20.
Hence, the total prize is '6x' because the ratio adds up to 6 parts (5:1). So, the total prize is '6 * 20 = £120'.