Problem
Use what was poured out to weigh the container
A container of milk has a known weight, and a known weight after some milk is poured out. We need the weight of the container alone.
Number systemExpressionsRatios
Your answer
How to solve
Strategy Identify Subproblems — Both weighings include the container, so subtracting one from the other cancels it and leaves pure milk. That gives the weight of a liter, and from there the container is what is left over.
1STEP 1
Subtract to remove the container
The difference between the two weighings is only the milk that was poured out, because the container is in both.
6.87 - 4.35 = 2.52
2.4 L of milk weighs 2.52 kg.
6.NS.B.3Identify SubproblemsThe difference between the two weighings is only the milk poured out.
Why?
Each weighing is the container plus the milk in it at that moment, and the container itself never changes.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Taking the second from the first therefore removes the container from both sides at once and leaves the milk that went.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Find the weight of one liter
Divide that weight by the number of liters poured out.
2.52 ÷ 2.4 = 1.05
One liter of milk weighs 1.05 kg.
6.RP.A.2Analyze The Units3STEP 3
Weigh the milk that was there at the start
Six liters at that weight each.
1.05 × 6 = 6.3
The milk alone was 6.3 kg.
6.RP.A.2Work Backwards4STEP 4
Take the milk off the first weighing
What is left of the first weighing is the container.
6.87 - 6.3 = 0.57
The empty container weighs 0.57 kg.
6.NS.B.3Identify SubproblemsAnswer
0.57 kg
Check the second weighing: 3.6 L of milk left is 1.05 × 3.6 = 3.78 kg, and 3.78 + 0.57 = 4.35 kg as stated.
Takeaway
Subtracting two measurements that share the same hidden weight makes that weight disappear.
- Subtract to remove the container
- Find the weight of one liter
- Weigh the milk that was there at the start
- Take the milk off the first weighing