A student solved this problem by working backwards.
Riley has some gerbils. He has 4 times as many as Lukas. Lukas has 2 gerbils. Riley gave 5 away and bought 2 more. How many gerbils does Riley have now?
Students's solution: Lukas has 2 gerbils, so Riley had 2 × 4 to begin with. So Riley had 8 gerbils. He gave away 5, so 8 – 5 = 3. He bought 2, so 2 + 3 = 5. So Riley has 5 gerbils.
Here is another problem that can also be solved by working backwards.
Maddy picked 2 times as many tomatoes as carrots from her garden. She picked 4 fewer cucumbers than tomatoes. Maddy picked 5 carrots.
How many cucumbers did Maddy pick?