Andy, Ben and Calvin had a total of 840 sweets. The ratio of the number of sweets Ben had to the number of sweets Calvin had was 1:4. After Andy and Ben each gave away 1/2 of their sweets, the three children had 620 sweets left. How many sweets did Ben have at first?
Let Ben begin with N sweets
Then Calvin had 4N sweets
And Andy had 840 - N - 4N = 840 - 5N sweets
When Andy and Ben each give away (1/2) of theirs we have
N / 2 + (840 - 5N)/2 + 4N = 620
N / 2 + 420 - (5/2)N + 4N = 620
420 + 2N = 620
2N = 620 - 420
2N = 200
N = 100 = the number that Ben had at first