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The Marble Ratio Brain Teaser
A bag contains red and blue marbles in the ratio 3 : 5. Someone adds 10 more red marbles, and now there are equal numbers of red and blue marbles. How many marbles were in the bag before the red marbles were added?
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What's the puzzle?
A bag contains red and blue marbles in the ratio 3 : 5. Someone adds 10 more red marbles, and now there are equal numbers of red and blue marbles. How many marbles were in the bag before the red marbles were added?
What's the answer?
40 marbles (15 red and 25 blue)
How do you work it out?
- At the start there are 3 parts red and 5 parts blue, so blue is 2 parts ahead of red.
- Adding 10 red marbles makes red and blue equal, so those 2 parts are worth 10 marbles.
- One part is 10 ÷ 2 = 5 marbles, so there were 3 × 5 = 15 red and 5 × 5 = 25 blue.
- The bag held 15 + 25 = 40 marbles before the extra red ones were added.
Frequently asked questions
Why does the blue count matter in the marble ratio puzzle?
In the marble ratio puzzle only red marbles are added, so the number of blue marbles stays the same. Spotting the quantity that does not change is often the key to ratio problems where a ratio moves from one value to another.
Can the marble ratio puzzle be solved with algebra?
Yes. Write the red marbles as 3k and the blue marbles as 5k, then solve 3k + 10 = 5k to get k = 5. LoveMaths Tutoring UK uses this puzzle to show that ratio parts and algebra lead to the same answer.
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