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2/5 of Zoe's money was 12 dollars more than 2/3 of Luke's money. When Zoe gave Luke 50 dollars, both of them had the same amount of money in the end. How much did Luke have at first?

 May 28, 2021
 #1
avatar+119887 
+1

Let  Z  =  what Zoe started with   and  L  =  what Luke started  with

 

(2/5)Z  =  (2/3)L  +  12          Multiply through by  15

 

6Z  = 10L  + 180

 

Z   =  (10L  + 180)  / 6          (1)

 

So

 

Z - 50   =  L  +  50    (2)         sub (1)  into (2)

 

(10L + 180)  / 6   -  50   =  L +  50

 

(5/3)L  + 30  - 50  = L + 50

 

(5/3)L - 20  =  L +  50

 

(5/3)L  - L  =  50 + 20

 

(2/3)L  =  70

 

L  =  70  (3/2)   =  $105   =  what Luke started with

 

 

cool cool cool

 May 28, 2021
 #2
avatar+36 
+1

z=zoe's money

l=luke's money

z-50=l+50

z=l+100

\(\frac{2l+200}5=\frac{2l}3+12\)

\(6l+600=10l+180\)

\(4l=420\)

\(l=105\)

so Luke had 105 dollars at first

 May 28, 2021

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