February 2025
Problem of the Month

Problem at the 7-11
Submitted by K. Sengupta, Calcutta, India

A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11.   He was curious that the cost was the same as the store name, so he enquired as to how the figure was derived.

The clerk said that he had simply multiplied the prices of the four individual items.   The customer protested that the four prices should have been ADDED, not MULTIPLIED.

The clerk said that that was OK with him, but, the result was still the same: exactly $7.11.

What were the four prices? (Do NOT count sales tax.)

Solution to the Problem:

Here is the solution:

The cost of the four items are
$ 1.20, $ 1.25, $ 1.50 and $ 3.16.

At the outset, we note that 711 is a positive integer multiple of 79, which is a prime number.  Accordingly, the cost of one of the items (in dollars) must be a positive integer multiple of 0.79. Let this cost be 0.79*n dollars and let the proice of the other three items be A, B and C (all in dollars).

Then, we have A+B+C = 7.11 - 0.79n and ABC = 9/n

Accordingly, we set up the following table:

n.......A+B+C .........ABC
1....... 6.32.............9.00
2....... 5.53.............4.50
3....... 4.74.............3.00
4....... 3.95.............2.25
5....... 3.16.............1.80
6....... 2.37.............1.50

Now, each of the other pairs with the exception of (3.95, 2.25)
(for n=4)would force one to create a round product from a non-round sum.

With a little trial and error, with:
(n, A+B+C, ABC) = (4, 3.95, 2.25), we observe that,
taking A = 1.50 gives(B+C, BC) = (2.45, 1.50), so that: (B, C) = (1.25, 1.20)

The price of the fourth item for n=4 is 0.79n = 3.16

Consequently, the cost of the four items are $ 1.20, $ 1.25, $ 1.50 and $ 3.16.

However, if we permit rounding, then there are numerous other answers.   So, Colin Bowey gets extra credit for sending the following answers:

Item 1 	Item 2 	Item 3 	Item 4 		 Sum 		Product 
$0.75	$1.96	$2.14	$2.26		$7.11		$7.11
$0.75	$1.96	$2.15	$2.25		$7.11		$7.11
$0.75	$1.96	$2.16	$2.24		$7.11		$7.11
$0.75	$1.97	$2.13	$2.26		$7.11		$7.11
$0.75	$1.97	$2.14	$2.25		$7.11		$7.11
$0.75	$1.98	$2.12	$2.26		$7.11		$7.11
$0.76	$1.86	$2.13	$2.36		$7.11		$7.11
$0.76	$1.86	$2.14	$2.35		$7.11		$7.11
$0.77	$1.79	$2.14	$2.41		$7.11		$7.11
$0.77	$1.80	$2.12	$2.42		$7.11		$7.11
$0.77	$1.80	$2.13	$2.41		$7.11		$7.11
$0.78	$1.73	$2.15	$2.45		$7.11		$7.11
$0.78	$1.74	$2.13	$2.46		$7.11		$7.11
$0.79	$1.68	$2.15	$2.49		$7.11		$7.11
$0.79	$1.69	$2.13	$2.50		$7.11		$7.11
$0.79	$1.69	$2.14	$2.49		$7.11		$7.11
$0.79	$1.70	$2.11	$2.51		$7.11		$7.11
$0.80	$1.65	$2.12	$2.54		$7.11		$7.11
$0.81	$1.61	$2.12	$2.57		$7.11		$7.11
$0.81	$1.61	$2.13	$2.56		$7.11		$7.11
$0.82	$1.57	$2.14	$2.58		$7.11		$7.11
$0.82	$1.58	$2.12	$2.59		$7.11		$7.11
$0.84	$1.51	$2.13	$2.63		$7.11		$7.11
$0.84	$1.51	$2.14	$2.62		$7.11		$7.11
$0.86	$1.46	$2.12	$2.67		$7.11		$7.11
$0.86	$1.46	$2.13	$2.66		$7.11		$7.11
$0.89	$1.39	$2.12	$2.71		$7.11		$7.11
$0.89	$1.39	$2.13	$2.70		$7.11		$7.11
$0.91	$1.35	$2.12	$2.73		$7.11		$7.11
$0.92	$1.33	$2.12	$2.74		$7.11		$7.11
$0.93	$1.31	$2.13	$2.74		$7.11		$7.11
$0.94	$1.29	$2.14	$2.74		$7.11		$7.11
$0.97	$1.25	$2.11	$2.78		$7.11		$7.11
$0.99	$1.22	$2.11	$2.79		$7.11		$7.11
$1.00	$1.21	$2.10	$2.80		$7.11		$7.11
$1.01	$1.19	$2.12	$2.79		$7.11		$7.11
$1.02	$1.18	$2.11	$2.80		$7.11		$7.11
$1.04	$1.15	$2.13	$2.79		$7.11		$7.11
$1.05	$1.14	$2.12	$2.80		$7.11		$7.11
$1.05	$1.14	$2.13	$2.79		$7.11		$7.11
$1.06	$1.13	$2.12	$2.80		$7.11		$7.11
$1.07	$1.12	$2.12	$2.80		$7.11		$7.11

Correctly solved by:

1. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
2. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
3. Davit Banana	Istanbul, Turkey
4. K M Thomas	Mumbai, India

Send any comments or questions to: David Pleacher