Reasoning · Grade 3-2 Measuring Capacity

Problem

Combine containers to hit a target capacity

Four containers hold 7 L 200 mL, 5 L 900 mL, 3 L 700 mL and 2 L 300 mL. Use two different containers once each to make a sum or a difference. Only one operation per attempt. Find which of the five targets cannot be made.
7 L 200 mL 5 L 900 mL 3 L 700 mL 2 L 300 mL
Your answer
How to solve
Strategy Make a Systematic List — There are only 6 possible pairs of containers, and each pair gives one sum and one difference, so 12 reachable amounts in all. Listing every reachable amount once makes it easy to check each target against the list. Converting every capacity to a single unit (mL) keeps the addition and subtraction clean.
1STEP 1

Convert all capacities to milliliters

In millilitres they are 7200, 5900, 3700, 2300.

7 L 200 mL = 7200 mL
2STEP 2

List every pair SUM

The six sums run from 6000 to 13100.

5900 + 2300 = 8200
3STEP 3

List every pair DIFFERENCE

The six differences run 1300 to 4900.

5900 - 3700 = 2200
4STEP 4

Check each target against the list

Missing from the list, 4800 and 9400 cannot be made.

4800 ∉ {reachable}, 9400 ∉ {reachable}
Answer
4 L 800 mL and 9 L 400 mL (cannot be measured)
The largest possible amount is A+B = 13 L 100 mL and the smallest non-zero is A-B = 1 L 300 mL, so every answer should fall in that range; 4 L 800 mL and 9 L 400 mL are in range yet simply never appear among the 12 reachable values, which is consistent with them being impossible. The three reachable targets each match an explicit pair, confirming the check.
Takeaway

List every amount two containers can make, then any target not on the list is impossible!

  • Convert all capacities to milliliters
  • List every pair SUM
  • List every pair DIFFERENCE
  • Check each target against the list