AMC 10 · 2009 · #1
Easy mode Grade 4Each can holds 12 ounces of soda. You need at least 128 ounces to make a full gallon. You can only use whole cans, not part of one. What is the fewest cans you need?
Pick an answer.
AMC 10 2009 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: One can holds 12 ounces of soda. A gallon is 128 ounces. Find the smallest number of whole cans whose soda adds up to at least 128 ounces.
Givens: Each can holds 12 ounces.; A gallon is 128 ounces.
Unknowns: The minimum number of cans needed to make at least 128 ounces.
Understand
Restated: One can holds 12 ounces of soda. A gallon is 128 ounces. Find the smallest number of whole cans whose soda adds up to at least 128 ounces.
Givens: Each can holds 12 ounces.; A gallon is 128 ounces.
Plan
Primary tool: #8 Analyze the Units
Secondary: #6 Guess and Check, #14 Extreme Principle
The problem links two units: ounces per can and total ounces needed. Track how ounces build up as cans are added, test whole numbers of cans against the 128-ounce target, and take the smallest count that reaches it.
Execute — Answer: E
4.OA.A.3 Step 1 Set the target
- Each can adds 12 ounces, so n cans hold 12 times n ounces.
- To make a gallon, that total must be at least 128 ounces.
💡 More cans means more ounces, so we just need enough cans to reach 128.
4.NBT.B.5 Step 2 Test 10 cans
- Try 10 cans.
- They hold 12 times 10, which is 120 ounces.
- That is less than 128, so 10 cans are not enough for a gallon.
💡 Ten is a round guess, but check the real ounces before trusting it.
4.NBT.B.5 Step 3 Test 11 cans
- Add one more can.
- Now 12 times 11 is 132 ounces, which is at least 128.
- So 11 cans make enough soda for a gallon.
💡 One more can adds 12 ounces, pushing the total just past 128.
4.OA.A.3 Step 4 Pick the smallest that works
- Ten cans fall short and eleven cans are enough, so the fewest cans that reach a gallon is 11.
- The answer is (E).
💡 The smallest whole number of cans that reaches the goal is the one right after it was still short.
4.OA.A.3 Each can adds 12 ounces, so n cans hold 12 times n ounces. To make a gallon, tha 4.NBT.B.5 Try 10 cans. They hold 12 times 10, which is 120 ounces. That is less than 128, 4.NBT.B.5 Add one more can. Now 12 times 11 is 132 ounces, which is at least 128. So 11 ca 4.OA.A.3 Ten cans fall short and eleven cans are enough, so the fewest cans that reach a Review
Reasonableness: A gallon of 128 ounces is a little more than ten 12-ounce cans, which give 120 ounces, so the count should be just above 10, and 11 fits. Eleven cans give 132 ounces, only 4 ounces of spare soda, matching a 'just barely enough' answer. The smaller choices 7, 8, 9, and 10 all give fewer than 128 ounces, so none of them can make a gallon.
Alternative: Divide 128 by 12 to get about 10.7 cans. Since you cannot buy part of a can, round up to the next whole number, 11.
CCSS standards used (min grade 4)
4.OA.A.3Solve multi-step word problems using four operations with whole numbers (Setting up the at-least-128-ounce goal and interpreting that the leftover forces rounding up to a whole number of cans.)4.NBT.B.5Multiply a whole number of up to four digits by a one-digit whole number (Computing 12 times 10 and 12 times 11 to see which count of cans reaches 128 ounces.)
⭐ When you can only buy whole items, work out how many you need and round UP so you have enough.
⭐ When you can only buy whole items, work out how many you need and round UP so you have enough.
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