Final answer:
Ann and Ethan will share the £420 prize in an 8:1 ratio, resulting in Ann receiving £373.36 and Ethan receiving £46.67.
Step-by-step explanation:
The student is asking how to divide a prize of £420 between Ann and Ethan in the ratio of 8:1.
To solve this problem, we need to find the total number of parts in the ratio, which is 8 + 1 = 9 parts.
Then, we calculate the value of one part by dividing the total prize amount by the total number of parts. So, one part equals £420 divided by 9, which is £46.67.
Next, we multiply the value of one part by the number of parts each person receives. Ann receives 8 parts, so she gets 8 × £46.67 = £373.36. Ethan receives 1 part, so he gets 1 × £46.67 = £46.67.
In conclusion, Ann receives £373.36 and Ethan receives £46.67 from the £420 prize, shared in an 8:1 ratio.