Concept 8 of 8
Balance Scales & Container Ratios
Today's big idea
Find the value of one small thing first, then multiply back up the chain.
Chain puzzles never measure the thing they ask you about directly.
How it works
👀 What's going on?
A puzzle tells you a bucket equals 5 bowls, and that 2 bowls hold 600 mL, then asks about 3 buckets. Nothing in it is measured directly, which is what makes it feel impossible at first.
💡 Here's the trick
Look at the chain above. It never tells you what a bucket holds. It does tell you 2 bowls hold 600 mL, so 1 bowl holds 300 mL. A bucket is 5 bowls, which makes 5 × 300 = 1500 mL. Every chain works this way: climb down to the smallest thing, price it, then multiply your way back up.
🪄 How to do it
- 1.List the links given in the chain above.
- 2.Work out the value of the smallest thing first.
- 3.Multiply up the chain until you reach what was asked.
✍️ Try it
- 1.3 pencils balance 1 ruler, and the ruler weighs 45 g. What does 1 pencil weigh?
- 2.A crate holds 4 tins, and 3 tins weigh 1 kg 200 g. What do 2 crates weigh?
The 3 pencils together weigh 45 g, so 1 pencil is 45 ÷ 3 = 15 g. For the crates, 1 tin is 1200 ÷ 3 = 400 g, so 1 crate is 4 × 400 = 1600 g. Two crates come to 3200 g, which is 3 kg 200 g.
⚠️ Watch out
You might be thinking that if 2 bowls hold 600 mL then 1 bowl holds 600 mL too. It does not. The 600 mL is shared between the two bowls, so each one holds 300 mL. Halve it before you build anything on top.
🌟 Why this matters
Recipes scale exactly like this when you double a batch, and so does working out the price of one pen from the price of six. A see-saw settles by the same rule. Getting down to the value of one thing is a habit worth keeping.
Exam tip: Write each link on its own line, then start on the line that already holds a real number.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“5 marbles balance 1 stone. The stone weighs 250 g. What do 4 marbles weigh?”
- 1
Find the smallest unit's value
5 marbles = 250 g, so 1 marble = 50 g.
- 2
Take the number asked
We need 4 marbles.
- 3
Multiply by 4
4 × 50 = 200 g
- 4
Answer ✓
= 200 g
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Swap the melon for its parts, one step at a time, until it is all cherries.
RATIO CHAIN · ROUND 1 OF 3
1 🍈 = 2 🍎
1 🍎 = 3 🍒
So 1 🍈 = ? 🍒
Quick check
✅ VERIFICATION
4 mugs fill 1 jug, and 3 jugs hold 6 L. How much does 1 mug hold?
⚡ Finish the activity above first to answer.
Keep going!