AMC 10 · 2025 · #1
Grade 5 arithmeticPick an answer.
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
Divide the total by one mug's share.
Sharing a total into equal-size portions is exactly what division counts.
4.OA.A.3Analyze The UnitsDivide 350 by 20
The quotient is 17 with 10 grams left over.
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 is discarded, so it is 17 mugs.
You cannot brew a fraction of a mug, so any leftover beans are simply wasted.
You cannot brew a fraction of a mug, so any leftover beans are simply wasted.
▸ Why?
Dividing leaves a remainder smaller than one portion, and that leftover cannot make another whole mug.
▸ Why?
One more mug would need more beans than are on hand, so the count stops at the whole part.
When 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