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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?

 Aug 27, 2023
 #1
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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

 Aug 27, 2023
 #2
avatar+128398 
+1

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

 

cool cool cool

 Aug 27, 2023

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