AMC 10 · 2025 · #1
Easy mode Grade 5A bag holds 350 grams of coffee beans. Making one large mug of coffee uses 20 grams of beans. Each mug must use the full 20 grams. What is the greatest number of full mugs you can make from the bag?
Pick an answer.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: A bag holds $350$ grams of coffee beans. Each properly brewed large mug uses exactly $20$ grams. Find the greatest number of full mugs you can make from the bag.
Givens: The bag contains $350$ grams of coffee beans; Each properly brewed large mug requires $20$ grams of beans; Answer choices: (A) $16$, (B) $17$, (C) $18$, (D) $19$, (E) $20$
Unknowns: The largest whole number of full mugs the $350$ grams can make
Understand
Restated: A bag holds $350$ grams of coffee beans. Each properly brewed large mug uses exactly $20$ grams. Find the greatest number of full mugs you can make from the bag.
Givens: The bag contains $350$ grams of coffee beans; Each properly brewed large mug requires $20$ grams of beans; Answer choices: (A) $16$, (B) $17$, (C) $18$, (D) $19$, (E) $20$
Plan
Primary tool: #8 Analyze the Units
Secondary: #14 Extreme Principle
The two numbers carry units: $350$ grams total and $20$ grams per mug. Tool #8 (Analyze the Units) shows that grams $\div$ 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.
Execute — Answer: B
4.OA.A.3 Step 1 Turn the words into a division
- You have $350$ grams and each mug eats up $20$ grams.
- To find how many $20$-gram portions fit inside $350$ grams, divide the total by the amount per mug.
- The units confirm the setup: grams $\div$ (grams per mug) leaves just mugs.
💡 Sharing a total into equal-size portions is exactly what division counts.
5.NBT.B.6 Step 2 Divide 350 by 20
- Carry out the division.
- $20\times17=340$ and $20\times18=360$, so $350$ sits between them.
- That means $350\div20=17$ with $10$ grams left over: $350-340=10$.
💡 Seventeen full scoops of $20$ use $340$ grams and leave a small remainder behind.
4.OA.A.3 Step 3 Round down to whole mugs
- The leftover $10$ grams is less than the $20$ grams a mug needs, so it cannot make an $18$th mug.
- The greatest number of full mugs is the whole part of the quotient, $17$.
- Trying $18$ would need $360$ grams, more than the bag holds, so $17$ is the boundary.
- The answer is $(\text{B})\ 17$.
💡 You cannot brew a fraction of a mug, so any leftover beans are simply wasted.
4.OA.A.3 You have $350$ grams and each mug eats up $20$ grams. To find how many $20$-gram 5.NBT.B.6 Carry out the division. $20\times17=340$ and $20\times18=360$, so $350$ sits bet 4.OA.A.3 The leftover $10$ grams is less than the $20$ grams a mug needs, so it cannot ma Review
Reasonableness: Check the boundary both ways: $17$ mugs use $17\times20=340$ grams, which fits inside $350$; $18$ mugs would need $18\times20=360$ grams, which overshoots the $350$ available. So $17$ is exactly the largest count that stays within the bag, matching (B). Choices (C)–(E) all demand more than $350$ grams, and (A) $16$ wastes a whole extra mug's worth of beans.
Alternative: Test the choices directly. Multiply $20$ by each: $16\to320$, $17\to340$, $18\to360$. The largest product that does not pass $350$ is $340$, from $17$ mugs, which again gives (B).
CCSS standards used (min grade 5)
5.NBT.B.6Find whole-number quotients with up to four-digit dividends and two-digit divisors (Dividing $350$ grams by the two-digit divisor $20$ grams per mug to get $17$ remainder $10$.)4.OA.A.3Solve multi-step word problems using four operations with whole numbers (Setting up the division from the word problem and interpreting the remainder so the answer is rounded down to whole mugs.)
⭐ 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.
⭐ 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.
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