Sue Pinion, Sandy McAdams, Lisa Stueve
7-11 Problem
A guy walks into a 7-11 store and selects four items to buy. The clerk
at the counter informs the gentleman that the total cost of the four items
is $7.11. He was completely surprised that the cost was the same as the
name of the store. The clerk informed the man that he had simply multiplied
all the costs of the items together to arrive at the total. The customer
calmly informed the clerk that the items should be added and not multiplied.
The clerk then added the items together and informed the customer that the
total was still exactly $7.11.What are the exact costs of the items?
Solution:
After looking at the number 7.11, one can see that the smallest exact decimal
divisor is .79. We decided to create a spreadsheet .
There are two rows, one denoting a sum and one denoting a product. In the
first row $.79 is placed and "random" values of the second two
numbers are changed. The fourth column is calculated from the first three
in order to come up with the correct sum. In the spreadsheet,
you will see the difference calculated also in the final value. The closer
this value comes to zero, the closer the values are to the exact costs of
the items.
After deciding that $.79 would never provide the desired exact values, we
decided to use multiples of $.79. The spreadsheet shows
the "best values" of each multiple, i.e. when the difference was
closest to zero. The last set of numbers shows that the solution is $3.16,
$1.20, $1.25, and $1.50.
Extension: Are there other numbers for which this is possible, i.e.
the sum of four positive integers is the same as their product?
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