Sarah and Henry share some sweets in the ratio 5:6 . Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 . How many sweets

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