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Puzzle Details:

I recently went to the shop and purchased 4 items.

Three of the items cost:

\$1.50
\$3.00
\$4.00

There was quite a long queue, and as I was quite bored, I was playing with my pocket calculator whilst waiting.

Very curiously, the 4 prices added to the same number as I got when I multiplied the 4 prices together.

What was the price of the 4th 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.

The answer can also be found using algebra. If we call the missing price P, we have:

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. QED.

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