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## Missing Price

Math brain teasers require computations to solve.

 Puzzle ID: #49348 Fun: (2.93) Difficulty: (1.1) Category: Math Submitted By: firefox99

When I went to the store, I purchased four items. The following shows the cost of three of the items:

\$1.50
\$3.00
\$4.00

The line to the checkout was pretty long, so to quench my boredom I started playing with my pocket calculator while waiting.

I found out, to my surprise, that the four prices of the four items I purchased added to the same number as I got when I multiplied the four prices together.

What was the price of the fourth item?

The three prices add to 1.50 + 3.00 + 4.00 = \$8.50.

The three prices multiply to 1.50 x 3.00 x 4.00 = \$18.00.

You might be able to see that adding another \$0.50 will take the total to \$9.00, and multiplying by another \$0.50 will take the product to \$9.00 also, but the answer can also be found using algebra. Let's call the unknown price P:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
8.50 + P = 18.00 x P
8.50 = 18.00 x P - P
8.50 = 17.00 x P
8.50/17.00 = P
P = 0.50.

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