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# Help

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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
+1

Call the total Number N

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

D + I =  (3/4)N             (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   Jul 6, 2022
#2
+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