A student solved this problem by working backward.

Tom had some marbles. He had three times as many marbles as Ralph. Ralph had 6 marbles. Tom lost 3 marbles and bought 6 new marbles. How many marbles does Tom have now?

Student's solution - Ralph has 6 marbles, so Tom has 6 × 3 marbles to begin with. So Tom has 18 marbles. He lost 3, so 18 – 3 = 15, and bought 6, so 15 + 6 = 21. So Tom now has 21 marbles.

Here is a problem that can also be solved by working backward.

Alex bought twice as many pears as apples. He bought 4 more pears than oranges. He bought 6 apples.

How many oranges did Alex buy?