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The ratio of Alan's apples to Don's apples was 3:5. When Alan gave 30 of his apples to Don, the ratio of Alan's apples to Don's apples became 1:5. Find the number of apples Alan had at first?

 May 27, 2021
 #1
avatar+69 
+2

Don's apples = D
Alan's apples = A
D = A * 1.666

A - 30 = (D -30)/5

A = 54
D = 90

Alan had 54 apples at first

 May 27, 2021
 #2
avatar+121047 
+2

A/ D   =   3/5       ⇒    D   =   (5/3)A         (1)            

 

A -  30                     1

_______    =          ___           cross-  multiply      

D  +  30                   5

 

 

5(A - 30)  =  D  +  30       (2)         sub  (1)  int  (2)

 

5 ( A  -  30)   =  (5/3)A  +  30       simplify

 

5A  -  150  =  (5/3)A  +  30

 

5A  - (6/3)A   =  30  +  150

 

(10/3)A  =  180

 

A   =  180  ( 3/10)   =     54  apples  at  frist

 

 

cool cool cool

 May 27, 2021
 #3
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0

Nice guest for copying the question here https://web2.0calc.com/questions/ratios_42

 

you did not write the question

 May 27, 2021

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