1994 AHSME Problems/Problem 5
Problem
Pat intended to multiply a number by but instead divided by
. Pat then meant to add
but instead subtracted
. After these mistakes, the result was
. If the correct operations had been used, the value produced would have been
Solution
We reverse the operations that he did and then use the correct operations. His end result is . Before that, he subtracted
which means that his number after the first operation was
. He divided by
so his number was
.
Now, we multiply by
to get
. Finally,
. Since
, our answer is
.
--Solution by TheMaskedMagician