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I need help to set up this proportion

 

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$.  When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes $18:7$.  How many students are in the class after these changes?

 Aug 4, 2023
 #1
avatar+128408 
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Call the number of original Juniors = J   Call the number of original Seniors = S

 

And we know that

J / S  = 3 / 2    so that   J = (3/2)S     (1)

 

When 6 more Juniors join and one Senior leaves, we  have

[ J + 6 ] / [ S -1 ]  =  18 / 7   (2)

 

Sub (1) into (2)

 

[(3/2)S + 6]  / [ S-1] =  18 / 7    cross-multiply

 

7 [(3/2)S + 6] =  18 [ S - 1]       simplify

 

(21/2)S + 42 = 18S - 18

 

42 + 18 =  18S - (21/2)S

 

60 = (36/2)S - (21/2)S

 

60 = (15/2)S   multiply through by 2

 

120 = 15S

 

S = 120 / 15  =  8 =  number of seniors in original class

 

J = (3/2)S  (3/2) (8)  =  12 =  number of Juniors in original class

 

After 6 Juniors join and 1 Senior leaves...we have the ratio  (12 + 6)  / (8 -1)  =  18 / 7

 

So....there are 25 total students in the  class after the changes

 

 

 

cool cool cool

 Aug 4, 2023

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