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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