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Daniel, Peter and Ivan had a collection of stamps. Peter and Ivan collected 9/16 of the stamps while Daniel and Ivan collected 3/4 of the stamps. Peter and David collected 55 stamps altogether. How many more stamps did Ivan collect than Peter?

 Jul 6, 2022
 #1
avatar+124676 
+1

Call the total Number N

 

P + I  = (9/16)N   →   (55 - D) + I  = (9/16)N      (1)  

D + I =  (3/4)N             (2)

 

Add (1) , (2)

 

55 + I + I  =  (9/16)N + (3/4)N

 

55 + 2I  =   (21/16)N

 

2I  =  (21/16)N -  55

 

I =  (21/32)N - 55/2

 

So

 

I + P + D  =  N

 

(21/32)N  - 55/2 +  55  =  N        multiply through by  32

 

21N + 880  = 32N

 

880  =  11N

 

N =  80

 

I =  (21/32) *80  - 55/2 =     25

 

P +  I =  (9/16) (80) =   45

 

P = 20

 

I - P  =    

 

25  - 20  =   5 

 

Ivan had 5 more than Peter

 

cool cool cool

 Jul 6, 2022
 #2
avatar+231 
+1

We assume Daniel collected x stamps

Peter collected y stamps

Ivan collected z stamps

So y + z + 9/16 (x + y + z)

     x + z = 3/4 (x + y + z)

     x + y = 55

x = 35

y = 20

z = 25

So z - y = 25 - 20 = 5

So the answer is 5 more stamps Ivan collected than Peter

 Jul 6, 2022

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