# High School Math

MISSION STATEMENT: To encourage and promote a greater use of the internet and computer technology in the math classroom. For educators, students, parents and homeschoolers.

## Sunday, April 03, 2005

### Stamps

Cynthia purchased almost 100 stamps today, in three different lots.
Some of her stamps cost 66 cents, some cost \$1.68, and some cost \$3.08.
She paid exactly the same amount for each lot.
How much did she pay for each lot?
` One possible solution is :Let the number of stamps in each lot be x, y, z.       Then 66x = 168y = 308z Factors of 66 are 2x3x11       of 168 are 2x2x2x3x7       of 308 are 2x2x7x11   Common factors of the three are 2x2x2x3x7x11 = 1848   Thus, 66x = 1848k, 168y = 1848k, 308z = 1848k where k is an integer. Then x = 28k, y = 11k, z = 6k. Now, x + y + z = 45k. And, since the number of stamps is almost 100, k must be equal to 2. Number of stamps in first lot is x = 28x2 = 56.                 in second lot is y = 11x2 = 22.                  in third lot is z = 6x2 = 12.   Total number of stamps is 56+22+12 = 90. Value of stamps in first lot is 66x56 = \$36.96.                in second lot is 168x22 = \$36.96.                 in third lot is 308x12 = \$36.96. If you have a shorter solution please submit as guest or comment.`

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