SOLUTION: Madison has a stamp collection of 3 cent stamps and 4 cent stamps. She has 3 less 4 cent stamps as 3 cent stamps. If the collection has a face value of 65 cents, how many of each d

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Question 1144548: Madison has a stamp collection of 3 cent stamps and 4 cent stamps. She has 3 less 4 cent stamps as 3 cent stamps. If the collection has a face value of 65 cents, how many of each does she have?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the number of 3-sent stamps.

Then the number of 4-cent stamps is (x-3), according to the condition.


   x pieces of 3-cent stamps have a total face value of 3x cents.

   (x-3) pieces of 4-cent stamps have a total face value of 4(x-3) cents.


Therefore, you can write the equation for a total face value of all stamps as


    3x + 4(x-3) = 65.


Simplify and solve for x.


    3x + 4x - 12 = 65

    7x           = 65 + 12 = 77

     x           = 77/7 = 11.


ANSWER.  11 3-cent stamps and (11-3) = 8 4-cent stamps.


CHECK.   3*11 + 4*8 = 65  cents.   ! Precisely correct !

Solved.

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There are other methods to solve this problem.

I showed you the simplest Algebra method here.