Astudent 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?