S + H = N
(5/11)N = s and (6/11)N = H <--- they are in the ratio 5:6 ; She has 5/11 of them and he has 6/11 of them.
She eats 24:
S-24 = (1/3)(N-24) <---Now the ratio is 1 to 2, so she has 1/3 of the remaining and he has 2/3
H = (2/3)(N-24)
H= (6/11)N = (2/3)(N-24) <-- Henry's amount does not change. so the two equations are equal.
18N = 22(N-24) <--- multiplies both sides by 33 to clear away the fractions
18N = 22N - 528 <--- distributive
0 = 4N - 528 <-- subtracts 18N from both sides
528 = 4N <--- adds 528 to both sides
N=132 <--- divides by 4
132 at the beginning....
She has 5/11*132 = 5 * 12 = 60 and he has 6/11 * 132 = 6 * 12 = 72.
She eats 24.
She then has 36 and he still has 72, which is in the ratio 1:2
Henry has 72 sweets
cited from wyzant
