Alice, Susan and Terry baked some cookies in the ratio of 5:9:11. After each of them gave 12 cookies to their mother, the ratio became 1:3:4. How many cookies did Terry bake?
A==Alice, S==Susan, T==Terry
A/S==5/9,
S/T==9/11,
[A - 12] / [S - 12]==1 / 3,
[S - 12] / [T - 12]==3 / 4, solve for A, S, T
A = 20 cookies - what Alice baked
S = 36 cookies - what Susan baked
T = 44 cookies - what Terry baked
+129771 5 : 9 : 11
Call the number of cookies baked = N
Alice baked 5 / ( 5 + 9 + 11) N = (5/25)N = (1/5)N
Susan baked 9/(5 + 9 + 11) = (9/25)N
Terry baked 11/ ( 5 + 9 + 11) = (11/25)N
After each gave 12 cookies to their mother Terry had (11/25)N - 12 left and this equals [ 4/ (1 +3 + 4)] ( N - 36)
So
(11/25)N - 12 = [4/ (1 + 3 + 4)] (N - 36)
(11/25)N - 12 = (4/8)(N - 36)
(11/25)N - 12 = (1/2)(N - 36)
(11/25)N - 12 = (1/2)N - 18
(22/50)N - 12 = (25/50) - 18
(25/50) N - (22/50)N = 18 - 12
(3/50)N = 6
N = (50/3) * 6 = 100
Terry baked (11/25)(100) = 44
Susan baked (9/25)(100) = 36
Alice baked (1/5)(100) = 20
After each gave 12 to their mother
Terry had 32
Susan had 24
Alice had 8
And 8 : 24: : 32 = 1 : 3 : 4
