Ruiya Math Blog · No. 5 · One Thinking Move
Equal value lets you exchange one thing for another.
A hard unit-price question becomes simpler when you stop trying to price both items at once. Replace equal-value packs until only one kind of item is left.
A Ruiya-original PSLE-style practice guide for Primary 5, Primary 6 and PSLE
The first useful observation
The question gives an exchange rule: 100 g of tea can be treated as one 300 g coffee pack in value.
One 100 g tea pack has the same value as one 300 g coffee pack. Eight equal-value packs cost $8.
The challenge
The tea-and-coffee challenge
- • 100 g of tea leaves costs the same as 300 g of coffee beans.
- • A shop sells 400 g of tea leaves and 1.2 kg of coffee beans for $8 altogether.
- • How much does 100 g of tea leaves cost?
This is a Ruiya-original analogue, not a past-paper question.
Why this strategy fits
Use a picture your brain already understands.
If one blue token can be exchanged for three yellow tokens at the game counter, you can rewrite a pile of blue and yellow tokens using just one colour before counting its value.
Break both quantities into matching packs. 400 g of tea is four 100 g tea packs. 1.2 kg of coffee is 1200 g, which is four 300 g coffee packs.
Use the equal-value swap. Each coffee pack has the same value as a tea pack. So the whole sale is worth eight equal tea packs.
Share the total value. $8 ÷ 8 = $1 per tea pack. Therefore 100 g of tea costs $1.
Check your answer
Four tea packs cost $4. Four equal-value coffee packs cost another $4. Together they cost $8.
Answer: 100 g of tea leaves costs $1.
Traps to watch for
The usual wrong turn is often a very reasonable first thought.
Mixing grams with price
The 100 g and 300 g packs are not equal in mass. They are equal only in value.
Forgetting 1.2 kg is 1200 g
Convert units before making packs, or the coffee count will be wrong.
Creating two unknown prices
The exchange rule is there to remove an unknown. Use it before writing complicated equations.
How an examiner can change it
Keep the thinking move, not the story.
The objects might be fruit boxes, ride tickets, phone-data bundles or containers. Look for ‘costs the same as’, ‘has equal value to’ or ‘can be exchanged for’. Those words offer a substitution shortcut.
Try a fresh variation
Two notebooks cost the same as three pens. Four notebooks and nine pens cost $42. What is the cost of one notebook?
Do not look for the same numbers. Ask which relationship is still doing the work.
Outside the exam
A useful model helps you make a fair decision.
Businesses compare equal-value bundles all the time: a family-size pack versus several small packs, reward points versus vouchers, or different data plans. Converting to one common unit makes the comparison fair.
Try it with Ruiya
Want help choosing the first step?
Send Ruiya a hard question and ask: “What is the relationship I should notice before I calculate?”
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