Is It a Sale?

This puzzle asks what makes a sale really a good deal.

A crowd gathered outside the electronics store. The window display was filled with radios, TVs, computers, and other electronic devices. The big sign in the window said, "Sale! 10% off."

"Not bad," declared one person in the crowd. "Everything is discounted 10%."

"Yes," said someone else, "but I came by here last week and they had just raised the prices by 10%. So there's really no sale. We're back where we started."

"No, there really is a sale," noted a third member of the group. "The final price is a bit lower than it was before the prices were raised."

Who is right?

Course:

Fractions [1]

Result/Solution(s)

Solution: Is It a Sale?

There is a small discount. Let’s say the original price of an item was 100 Seedos. (The Seedo is the unit of currency in Seedonia, where this took place.) When the price was raised 10%, it became 110 Seedos. Next there was the sale with a 10% reduction. Since 10% of 110 is 11, the reduction would be 110 – 11 = 99. The sale price would be 99 Seedos, a savings of 1 Seedo off the original price.

In general, a 10% markup followed by a 10% discount ends up with a 1% savings. Here’s another example: The original price is 500 Seedos. After a 10% increase the price is 550 Seedos. Now a 10% discount brings it down by 55 Seedos to 495 Seedos. This is a savings of 5 Seedos, which is 1% of the original price.

What would happen if the markup and discount were both 20%? What about 30%?

Percents puzzle [2]
fractions puzzle [3]