# How Much Profit?

Math Lair Home > Puzzles & Problems > How Much Profit?

Here are two problems; one has a simple mathematical solution, and the other doesn't have a clear-cut solution. Most people can come up with an answer to each of them. Frequently, however, (for the first problem, especially when some of the members of the group are not mathematically literate), people will come up with several different answers, and defend them vigourously, resulting in a big argument!

A person bought an item for \$6, and then sold that item for \$7. The person then bought the item back for \$8, and sold it again for \$9. How much profit did the person make?

It's a pretty straightforward problem:

Profit = Revenue − Expenses
Profit = \$9 + \$7 − \$8 − \$6
Profit = \$2

... but oftentimes people will come up with different answers. Give it a try with your friends and see how it goes.

The following problem isn't as clear:

A person sold an item for \$7. The person then bought the item back for \$8, and sold it again for \$9. How much profit did the person make?

Obviously, the person made \$1 on the purchase for \$8 and sale for \$9. But how much profit did the person make on the first sale? Did he break even? Make money? Lose money? Without knowing the value of the item, we can't say whether the first sale made or lost money. If the item is worth \$6, then he made \$1 on the sale. If the item is worth \$10, then he lost \$3 on the sale. Further complicating matters is that most real-world objects don't have an intrinsic value, just whatever price a buyer and a seller can agree on. Again, this problem can result in a vigourous argument.

Sources used (see bibliography page for titles corresponding to numbers): 31, 32.