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7-11 Problem

A woman walks into a 7-11 and takes four items to the cash register. The clerk informs her that the register is broken, but he can figure the total using his calculator. The clerk then proceeds to multiply the prices together and declares that the total is $7.11. Although the woman knows the prices should have been added, not multiplied, she says nothing — as it turns out, the result would have been $7.11 whether the four prices were added or multiplied.

There was no sales tax. What was the cost of each item?

Less Difficult

A simpler version of this problem, which can be solved with a system of linear equations, employs the following modifications:

  • There are two items instead of four.
  • The total cost is $8.41, not $7.11.
But everything else is the same — the total price is the same whether the clerk mutliplies or adds, and there's still no sales tax.