### 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?

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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.

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