AMC 10 · 2017 · #1
Grade 4 arithmeticPick an answer.
Tool #14 (Extreme Principle): the question asks for the greatest number of popsicles, so push toward the most popsicles per dollar and use every dollar. Tool #8 (Analyze the Units): what really matters is popsicles per dollar, so compare the three deals on equal footing before buying anything. Tool #6 (Guess and Check): after building the best buy, test a few other ways to split the $8 to make sure none of them gives more.
Compare the three deals
At a common price the big box wins.
Judging deals at the same price tag shows which one stretches a dollar the furthest.
Judging the deals at the same price tag shows which one stretches a dollar the furthest.
▸ Why?
Each box charges a fixed price for a fixed bundle, so the value is a count per unit of money.
▸ Why?
Once the rates are ranked, the best one stays best however many boxes are bought.
Buy the best box as much as possible
Buying it twice gives 10 and leaves change.
Loading up on the best deal first squeezes the most popsicles out of most of the money.
4.NBT.B.4Extreme PrincipleSpend the last two dollars
The leftover buys 3 more.
Even the leftover money should go to the better popsicles-per-dollar choice.
4.NBT.B.4Analyze The UnitsCheck no split beats 13
No other split beats 13, choice (D).
Trying the natural rivals confirms the best buy really is the biggest.
4.OA.A.3Guess And CheckFind the best popsicles-per-dollar deal, buy as many as you can, then spend the leftover on the next-best deal: two 2 box make 13 popsicles — choice (D).
- Compare the three deals
- Buy the best box as much as possible
- Spend the last two dollars
- Check no split beats 13