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?
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
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