stamp word question

Question

a collection of stamps consists of 3 cents stamps, 7 cents stamps, and 12 cents stamps. The number of 3 cents stamps is five less than the number of 7 cents stamps. The number of 12 cents stamps is one-half the number of 7 cents stamps. The total value of all the stamps is $2.73. Find the number of each type of stamp in the collection.

Answer 1

Let x = number of 3 cent stamps

      y = number of 7 cent stamps

      z = number of 12 cent stamps

 

x = y - 5

z = 0.5y

0.03x + 0.07y + 0.12z = 2.73

 

Substitute for x and z in the third equation:

 

   0.03(y - 5) + 0.07y + 0.12(0.5y) = 2.73

 

   0.03y - 0.15 + 0.07y + 0.06y = 2.73

 

                                           0.16y = 2.88

 

                                                  y = 18     So, x = y - 5 = 13

                                                                        z = 0.5y = 9