Answer:
The total sum of money is £810
Step-by-step explanation:
The parameters given are;
The ratio of the sum Anne, Becky and Charlotte had = 7:6:5
One of them gave one of the others £9 and the new ratio becomes 6:5:4
The total sum of money remains the same = M
The initial fraction amount of the total sum of money each had is given as follows;
Anne = 7/(7 + 6 + 5)×M = 7/18·M = 0.389·M
Becky = 6/18·m = 1/3·M
Charlotte = 5/18·M = 0.278·M
After one of them gave £9 to one of the others, the fraction amount of the total sum of money each had became;
Anne = 6/(6 + 5 + 4)×M = 6/15·M = 0.4·M
Becky = 5/15·m = 1/3·M
Charlotte = 4/15·M = 0.267·M
Therefore, given that Anne's fraction of the total sum of money increased while Charlotte's fraction of the total sum of money decreased, it was Charlotte that gave Anne £9
Therefore, the fraction of the total sum of money equivalent to £9 is found s follows;
5/18·M - 4/15·M = 1/90·M = £9
Therefore;
M = 90 × £9 = £810
The total sum of money = £810.
