AMC 10 · 2025 · #1
Grade 5 arithmeticPick an answer.
AMC 10 2025 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The two numbers carry units: 350 grams total and 20 grams per mug. Tool #8 (Analyze the Units) shows that grams ÷ grams-per-mug cancels to give a count of mugs, so a single division does the work. Because the question asks for the greatest number of full mugs and leftover beans cannot fill another mug, Tool #14 (Extreme Principle) says to push to the boundary and round the quotient down to a whole number rather than up.
Turn the words into a division
Fitting 20-gram portions inside 350 grams is a division: grams ÷ grams-per-mug cancels down to just mugs.
Sharing a total into equal-size portions is exactly what division counts.
Sharing a total into equal-size portions is exactly what division counts.
▸ Why?
The whole is those equal portions repeated, which is what multiplying records.
▸ Why?
Counting how many whole portions fit is a division, and what is left over is the remainder.
Divide 350 by 20
20×18=360 overshoots 350 while 20×17=340 fits, so the division gives 17 remainder 10.
Seventeen full scoops of 20 use 340 grams and leave a small remainder behind.
5.NBT.B.6Analyze The UnitsRound down to whole mugs
The leftover 10 grams cannot fill a mug that needs 20, so round the quotient down: the answer is (B) 17.
You cannot brew a fraction of a mug, so any leftover beans are simply wasted.
4.OA.A.3Extreme PrincipleWhen you split a total into fixed portions and only whole ones count, divide and then round down — leftovers that are too small to fill another portion just get left behind.
- Turn the words into a division
- Divide 350 by 20
- Round down to whole mugs