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.
I used the Windows calculator. No algebra needed. I first tried 1 for the fourth price, and when that was too high, I went with .5, which luckily turned out to be exactly right.
Easy teasy. Nice quick puzzle you can through at people interactively.
I'm guessing you're not still wondering after posting your comment 7 years ago, but J-Mac, 18 x P - P = 17 x P, b/c...
18 x P is actually 18P (think of P as a unit, and you have 18 of them)
Then you subtract P, which is 1P (again, as a unit, you have 1 of them)
If you have 18P and you subtract 1P, you get 17P (or 17 x P)
Hopefully that makes sense to you or anyone else reading who didn't understand that. Take care!
Oh, and the teaser was good. I wish it was a little harder, but I still enjoyed it.
18 x P is actually 18P (think of P as a unit, and you have 18 of them)
Then you subtract P, which is 1P (again, as a unit, you have 1 of them)
If you have 18P and you subtract 1P, you get 17P (or 17 x P)
Hopefully that makes sense to you or anyone else reading who didn't understand that. Take care!
Oh, and the teaser was good. I wish it was a little harder, but I still enjoyed it.
"Livigs": Thanks for your excellent explanation regarding "P"; I was wondering the same!
I think my algebra needs brushing up?
Gr8 teaser BTW, thank you!
I think my algebra needs brushing up?
Gr8 teaser BTW, thank you!
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