AMC 10 · 2014 · #1
Grade 3 algebraPick an answer.
The clean fact is about a made-up future: after adding one nickel the counts are equal. So Tool #11 (Work Backwards) is natural — first describe that easy equal-split state, then undo the added nickel to recover how many pennies and nickels Leah really has. Tool #8 (Analyze the Units) keeps the money straight at the end: a nickel counts as 5 cents and a penny as 1 cent, so the total must be measured in cents, not in coins.
Split the pretend total in half
The pretend total splits evenly into 7 and 7.
"Same number of each" out of a known total just means split the total into two equal groups.
The same number of each kind out of a known total just means splitting that total into two equal groups.
▸ Why?
Two equal groups are two equal shares of the whole, so each group is half of it.
▸ Why?
The pile is exactly its two kinds put together, so their counts have to fill it completely.
Undo the extra nickel
Removing the imagined coin restores the real counts.
To reverse a step, remove exactly what was added and leave everything else alone.
2.OA.A.1Work BackwardsAdd up the money in cents
Adding the money gives 37, choice (C).
Coins of different kinds only add up correctly once you turn each into its cent value first.
2.MD.C.8Analyze The UnitsWhen a condition describes an imagined future, build that easy picture first, then undo the change to see what is really true now.
- Split the pretend total in half
- Undo the extra nickel
- Add up the money in cents