Frank, mary and seth shared some sweets in the ratio 4 : 5 : 7 seth got 18 more sweets than frank. work out the total number of sweets they shared.

So, Seth has 18 more sweets than Frank, yet theres only 3 number difference in the ratio, 4:5:7   (4:5) 3 number difference, 18/3= 6

add the ratios = 4+5+7= 16
1 number = 6 so 
4x6= 24
5x6=30
7x6=42

Frank gets 24 sweets
Mary gets 30 sweets
Seth gets 42 sweets

The total number of sweets they shared is 24+30+42= 96
The share 96 sweets altogether. 

The check your answer; do 42-24= 18

Therefore, now we know that the difference between Seth and Frank's amount of sweets is 18.

Therefore, this is correct.