POD - Rob's Stamps

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RESIST TEMPTATION!! 
DO NOT USE GUESS-and-CHECK!

Set up and solve algebraically!

Using 32-cent, 20-cent and 7-cent stamps, Rob put $10.08 of postage on a large package.  He used twice as many 32-cent stamps as 20-cent stamps and three times as many 7-cent stamps as 32-cent stamps.  How many of each type of stamp did he use?

 

 

  answer

 

 

 

 

 

 

 

Solution:

Let x = # of 20-cent stamps

Let y = # of 32-cent stamps

Let z = # of 7-cent stamps

So, we have the equation:

.20x + .32y + .07z = 10.08

Upon further review, we can say that:

the # of 32-cent stamps, y = 2x
the # of 7-cent stamps,   z = 3y = 6x

Using substitution:

.20x + .32(2x) + .07(6x) = 10.08  <<mult by 100>>

20x + 32(2x) + 7(6x) = 1008  <<simplify each term>>

20x + 64x + 42x = 1008  <<combine like terms>>

126x = 1008

x = 1008/126

x = 8

therefore, Rob used:

  8  20-cent stamps
16  32-cent stamps
48    7-cent stamps

 

Check your answer in the original problem:

.20(8) + .32(16) + .07(48) = 10.08

1.60 + 5.12 + 3.36 = 10.08  TRUE!

 

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