SOLUTION: A stamp collection consists of 5, 13, and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. The number of 18 cent stamps is five more

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Question 25612: A stamp collection consists of 5, 13, and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. The number of 18 cent stamps is five more than the number of 13 cent stamps. The total value of all stamps is $2.60. Find the number of 13 cent stamps in the collection.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 5 cent stamps be x
Let the 13 cent stamps be y
Let the 18 cent stamps be z
y = 2x-1---->2x-y=1 (equation 1)
z = 2x-1+5-->2x-z=-4 (equation 2)
5x+13y+18z=260 (equation 3)
Eliminate z
to eliminate z multiply the second equation by 18
5x+13y+18z=260
36x-18z=-72
--------------
41x+13y=188 (set 1)
Multiply equation 1 by 13 and THEN add Set 1 by equation 1
41x+13y=188
26x-13y=13 (y eliminated)
67x=201
x=3
Solve for y
y=2(3)-1
y=5
z=2(3)-1+5
z=10

Hence, there were 3 five cents stamp, 5 thirteen cent stamps, and 10 eighteen cent stamps.
Paul.