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.

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!