KA-0050Working backwards
3 points, difficulty 1 of 3Level 3–4about 60sToma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Undo the last step first.
2The strategy
The halving happened after the 4 euros were spent, so undo the halving before you put the 4 back. Doubling comes first, adding comes second.
3The full solution
She had 6 after spending half, so she had 12 before that. Adding back the first 4 euros gives 16.
Solution— no shortcut on this one
Run the story backwards. She ends with 6 euros, which is half of what she had after the first purchase, so she had 12 at that point. Before the first purchase she had 12 + 4 = 16. Check forwards: 16 - 4 = 12, half of 12 is 6. The transferable idea: reverse the operations and the order together.
Why this is on the test: It is the same working-backwards shape with the halving in a different position, which is where students who memorised a recipe rather than the method fail.