Here's a fun problem I ran into the other day....I don't even know * WHAT *the answer is....!!!....but, maybe some creative folks on here would like to propose a solution....heck......there might be even

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In the US, we have these convenience stores known as "7-11's"....well, anyway....

A man goes into a 7-11 and picks up three items and takes them to the clerk.

He asks the clerk, "How much?"

The clerk says, "I multiplied the prices together, and it comes to $7.11."

The man says, "* Multiplied*??....you were supposed to

The clerk says, "Doesn't make much difference. Adding them together produces the * same* total.'

The question is......what are the possible prices of the three items???

Have fun....!!!

CPhill Jan 22, 2015

#6**+15 **

$$\small{\text{The best solutions: $< 0.001$ \$ difference }}\\\\

\small{\text{

$

\begin{array}{rcccr}

\# & & & & \small{\text{difference in \$ }} \\

1. & \$ 4.22 & \$ 2.08 & \$ 0.81 & 0.000144 \\

2. & \$ 3.21 & \$ 3.21 & \$ 0.69 & 0.000171 \\

3. & \$ 4.62 & \$ 1.35 & \$ 1.14 & -0.000180 \\

4. & \$ 3.22 & \$ 3.20 & \$ 0.69 & 0.000240 \\

5. & \$ 4.37 & \$ 1.87 & \$ 0.87 & 0.000447 \\

6. & \$ 3.23 & \$ 3.19 & \$ 0.69 & 0.000447 \\

7. & \$ 3.85 & \$ 2.53 & \$ 0.73 & -0.000565 \\

8. & \$ 4.25 & \$ 2.04 & \$ 0.82 & 0.000600 \\

9. & \$ 3.24 & \$ 3.18 & \$ 0.69 & 0.000792

\end{array}

$

}}$$

(by Computing)

heureka Jan 23, 2015

#2**+10 **

**......what are the possible prices of the three items : $$\\ \$\ 4.62 \qquad \$\ 1.35 \qquad \$\ 1.14 \\ \dots$$**

heureka Jan 23, 2015

#4**+15 **

Here are a couple of other solutions (though all are approximate, including heureka's, as the products are only accurate to just under 2*10^{-2} of a cent!):

$0.69 $3.21 $3.21

$0.81 $2.08 $4.22

Solutions obtained by brute force and ignorance! (i.e. running through all possibilities to the nearest cent, from 1cent to $7.11, for two of the items and calculating the third by subtracting the sum from $7.11, then checking to see if the product differs from $7.11 by less than 0.02cents - I didn't do this by hand of course!

I found no solutions when looking for a product that differs from $7.11 by less than 0.01 cents).

.

Alan Jan 23, 2015

#5**0 **

"Brute Force" and "Ignorance" are two of my favorite math techniques....in fact, I would feel lost without them....!!!

Thanks, Alan...for those answers....

CPhill Jan 23, 2015

#6**+15 **

Best Answer

$$\small{\text{The best solutions: $< 0.001$ \$ difference }}\\\\

\small{\text{

$

\begin{array}{rcccr}

\# & & & & \small{\text{difference in \$ }} \\

1. & \$ 4.22 & \$ 2.08 & \$ 0.81 & 0.000144 \\

2. & \$ 3.21 & \$ 3.21 & \$ 0.69 & 0.000171 \\

3. & \$ 4.62 & \$ 1.35 & \$ 1.14 & -0.000180 \\

4. & \$ 3.22 & \$ 3.20 & \$ 0.69 & 0.000240 \\

5. & \$ 4.37 & \$ 1.87 & \$ 0.87 & 0.000447 \\

6. & \$ 3.23 & \$ 3.19 & \$ 0.69 & 0.000447 \\

7. & \$ 3.85 & \$ 2.53 & \$ 0.73 & -0.000565 \\

8. & \$ 4.25 & \$ 2.04 & \$ 0.82 & 0.000600 \\

9. & \$ 3.24 & \$ 3.18 & \$ 0.69 & 0.000792

\end{array}

$

}}$$

(by Computing)

heureka Jan 23, 2015