Ashopper seeking a bargain combined a 25% off coupon with the store's existing 25% off sale, and brought enough money to cover 50% of the base price. why did this shopper go home disappointed

Because the % discounts cannot be added to calculate the final price.

The first discount is over the original price but the second discount is over the already discounted price.

You can find a combined factor if you multiply the two factors.

Discount of 25% => Factor = 0.75

Now you can find the combined factor by multilplying 0.75*.75 = 0.5625

That means that the final price will be the original price times 0.5625 (or what is the same that the discount is 100 - 56.25 = 43.75%.

Then the operation results in a higher price than if you multiply by 0.5 (50% discount).

In conclusion the discount resulting from two consecutive 25% discounts is less than a 50% discount.