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1/5 of Andrew's money was $12 more than 1/3 of Drake's money. When Andrew have Drake $50, both of them had the same amount of money in the end. How much did Andrew have at first?

 Apr 20, 2021
 #1
avatar+290 
+1

1/5 of Andrew' money = 1/3 of Drake's money + $12


3/5 of Andrew's money = 3/3 of Drake's money + $36

 

Difference at first --> 2/5 of Andrew's money + $36

 

Difference at first --> $50 * 2

                              = $100


2/5 of Andrew's money + $36 = $100

$100 - $36 = $64

2/5 of Andrew's money = $64

 

1/5 of Andrew's money = $32

Andrew's money = $32 * 5

                            = $160


Andrew had $160 at first.

 Apr 20, 2021
 #2
avatar+121006 
+1

(1/5)A  - 12   =  (1/3)D      multiply through  by  3

 

(3/5)A  - 36  =  D       (1)

 

A  - 50  =  D  + 50     (2)

 

Sub (1)  into  (2)  for D

 

A - 50 =  (3/5)A -  36 + 50

 

A - (3/5)A  =  - 36  + 50 + 50

 

(2/5)A  = 64

 

A = 64 (5/2)  =  160  (dollars)  = what  Andrew  started with

 

Proof

 

(1/5)A  - 12  = (1/3) D

 

(1/5)A   -12 =  (1/3)((3/5)A  - 36 ]

 

32  - 12  =   (1/3) ( 96 - 36]

 

20  =  (1/3) 60

 

20   = 20

 

 

cool cool cool

 Apr 20, 2021

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