### Brain Teasers

# Missing Price

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?

$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?

### Hint

Add and multiply what you have already.### Answer

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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## Comments

Good one but pretty easy .... keep them coming ...cheers....

like these easy fun ones..keep em coming!

No comment!

yeah it is easy

Nice and easy, perfect for a Sunday morning

Not bad, but not much of a challenge, eh?

Cool, but not much tasking.

Cool, but not much tasking.

simple, but at least got the juices flowing!

I got the answer in seconds without using a calculator or paper and pen. Pretty easy. I like math problems, but this one was too easy.

Thanks for the puzzle! It was fairly easy to just figure it out without any formulae, but your algebra work has me stumped. All is fine until you go from:

8.50 = 18.00 x P - P

to...

8.50 = 17.00 x P

How do you get to 17.00 when dropping off the "- P"?

Jim

8.50 = 18.00 x P - P

to...

8.50 = 17.00 x P

How do you get to 17.00 when dropping off the "- P"?

Jim

The algebra approach is quite predictable. What would be interesting would be for solvers to explain HOW they did it in "a few seconds"! I enjoyed this puzzle, even though it is easy.

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