Since all of the pens costs $102, we have:
xy = 102. . . . . . . . . . . . . . . . . . . . . . . . . .(1)

Then, he sold all but three pens for $2.50 more each and made $99. This yields:
(x - 3)(y + 2.5) = 99. . . . . . . . . . . . . . . . . . (2)

By expanding (2):
(x - 3)(y + 2.5) = 99
==> xy + 2.5x - 3y - 7.5 = 99
==> 102 + 2.5x - 3y - 7.5 = 99, since xy = 102 from (1)
==> 2.5x - 3y = 4.5
==> 5x - 6y = 9. . . . . . . . . . . . . . . . . . . . .(3)

From (1), y = 102/x, so:
5x - 6(102/x) = 9
==> 5x^2 - 9x - 712 = 0, by multiplying both sides by x
==> (5x + 51)(x - 12), by factoring
==> x = -51/5 and x = 12, by the zero-product property.

Since Matt cannot buy a negative number of pens, x = 12.

Since Matt sold all but three pens, he sold 12 - 3 = 9 pens.

I hope this helps!

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