SOLUTION: A collection of stamps consist of 3¢ stamps, 7¢ stamps, and 12 ¢ stamps. The number of 3 ¢ stamps is five less than the number of 7 ¢ stamps. The number of 12 ¢ stamps is one-half

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Question 1040717: A collection of stamps consist of 3¢ stamps, 7¢ stamps, and 12 ¢ stamps. The number of 3 ¢ stamps is five less than the number of 7 ¢ stamps. The number of 12 ¢ stamps is one-half the number of 7 ¢ stamps. The total value of all the stamps is $2.73. Find the number of each type of stamp in the collection.
Found 4 solutions by stanbon, josmiceli, ikleyn, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A collection of stamps consist of 3¢ stamps, 7¢ stamps, and 12 ¢ stamps.
The number of 3 ¢ stamps is five less than the number of 7 ¢ stamps.
t = s - 7
----------------
The number of 12 ¢ stamps is one-half the number of 7 ¢ stamps.
w = (1/2)s
---------------------------
The total value of all the stamps is $2.73.
t + s + w = 273
Find the number of each type of stamp in the collection.
--------------------
Substitute for "t" and for "w" and solve for "s"::
s-7 + s + (1/2)s = 273
----------------------------
(5/2)s = 280
s = 2*56
s = 112
----
t = s-7 = 105
----
w + s/2 = 56
-----------------
Cheers,
Stan H.
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Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of 3 cent stamps
Let = number of 7 cent stamps
Let = number of 12 cent stamps
----------------------------------
(1)
(2)
(3) ( in cents )
-----------------------------------
Substitute (1) and (2) into (3)
(3)
(3)
(3)
(3)
and
(1)
(1)
(1)
and
(2)
(2)
(2)
-----------------------
The number of 3 cent stamps is 13
The number of 7 cent stamps is 18
The number of 12 cent stamps is 9
------------------------------
check:
(3)
(3)
You can verify this equation
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
I confirm the solution by the tutor "josmiceli"

The number of 3 cent stamps is 13
The number of 7 cent stamps is 18
The number of 12 cent stamps is 9


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A collection of stamps consist of 3¢ stamps, 7¢ stamps, and 12 ¢ stamps. The number of 3 ¢ stamps is five less than the number of 7 ¢ stamps. The number of 12 ¢ stamps is one-half the number of 7 ¢ stamps. The total value of all the stamps is $2.73. Find the number of each type of stamp in the collection.
Are you serious, Stanbon? You "gotta" be kidding me!! Do you really tutor? 

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