One of the best ways to negotiate this problem is to use a variable for the "unknown," the number of heads of lettuce sold each day. Call this number n. Now we can follow the problem either forward or backward.
Following it forward:
Start of first day: 80.
End of first day: 80  n.
Start of second day: 2(80  n) = 160  2n.
End of second day: 160  2n  n = 160  3n.
Start of third day: 3(160  3n) = 480  9n.
End of third day: 480  9n  n = 480  10n. Since this equals zero, 480  10n = 0, and this means 480 = 10n, and 48 = n.
Following it backwards:
End of third day: 0
Start of third day: n
End of second day: 1/3 n [the stock was tripled!]
Start of second day: 1/3 n + n = 1 1/3 n
End of first day: 2/3 n [half of 1 1/3]
Start of first day: 2/3 n + n = 1 2/3 n = 80 heads. So n = 80 divided by 1 2/3 = 48.
Notice that backtracking seems to be a little easier here. A solution obtained by covering up is possible, but it would be more difficult because it would require you to write an equation for the entire problem in which there is only one variable.
You could also use false position and decide whether the number of heads sold in a day was too small (if some were left at the end), too large (if not enough were left to be sold on the third day), or just right (48). In this problem, though, false position amounts to guessandcheck, because there is no easy way to adjust a wrong answer to make a right one.
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