The hot dog costs $3.00 more than the soda.
How much does the soda cost?
💡 Hint
Let one letter stand for the soda’s price and write the hot dog’s price in terms of it. Then check that the two prices add up to the full total.
Reveal answer
The soda costs 15 cents, and the hot dog costs $3.15.
Step-by-step solution
- Let the soda cost S dollars. The hot dog costs $3.00 more, so it costs S + 3.00.
- Together they cost $3.30: S + (S + 3.00) = 3.30, which simplifies to 2S + 3.00 = 3.30.
- Subtract 3.00 from both sides: 2S = 0.30, so S = 0.15. The soda costs 15 cents and the hot dog costs $3.15.
- Check both conditions: $3.15 + $0.15 = $3.30, and $3.15 is exactly $3.00 more than $0.15. Both hold.
- Check the tempting answer too: a 30-cent soda makes the hot dog $3.30, so the pair costs $3.60. The gap is right, but the total is 30 cents too high.
Why it fools people
The question is built so that the wrong answer arrives first and feels complete. Subtracting $3.00 from $3.30 uses both numbers, gives a tidy result and takes no effort, so the mind accepts it without testing it. The flaw is that “$3.00 more than the soda” describes a gap, not a price. Once the $3.00 gap is set aside, the 30 cents that remain have to be split between two items, not handed to one of them.
Did you get it?
About This Puzzle
It’s the seventh-inning stretch, the line at the concession stand is long, and you overhear two prices that sound almost too simple to bother with. This puzzle takes about ten seconds to read and about two seconds to get wrong. It’s a ballpark retelling of one of the most studied questions in psychology, used by researchers to show how quickly a confident first answer can push careful thinking aside. You don’t need anything beyond basic arithmetic, and you don’t need a calculator. You need one thing that is surprisingly hard to do: pause, and check whether the answer that just popped into your head actually satisfies both facts in the question.
How to Think About It
An answer will probably arrive before you finish reading. Treat it as a guess, not a result. A good habit with any word problem is to list the conditions separately and test your guess against each one. Here there are two: the prices must add up to $3.30, and the gap between them must be exactly $3.00. If your guess passes the first test but fails the second, stop guessing and write a tiny equation. Call the soda price S, write the hot dog price in terms of S, and let the total do the work. Then check the result against both conditions again.
Common Traps
The trap is a number that fits one condition perfectly and quietly ignores the other. Your brain sees $3.30, sees $3.00, and reaches for the fastest operation that turns two given numbers into a third. The result feels right because it uses every number in the problem and comes out clean. Another common slip is to rough out the split in your head and round to something that looks like a real concession price. Real prices don’t matter here. Only the two conditions do, and a correct answer has to pass both of them at once.
Where This Puzzle Comes From
The original version uses a bat and a ball that cost $1.10 together. It became famous through psychologist Shane Frederick’s 2005 paper on the Cognitive Reflection Test, a three-question quiz designed to measure whether people override a quick intuitive answer. Many students at highly selective universities gave the fast wrong answer. The lesson is not that people are bad at arithmetic. It’s that fluent answers are persuasive, and a five-second check is the cheapest insurance there is.
Try This Variation
Same stadium, bigger order. A large pizza and a tray of wings cost $21.50 together, and the pizza costs $15.00 more than the wings. How much do the wings cost?
Show the answer to the variation
The wings cost $3.25 and the pizza costs $18.25. Set aside the $15.00 gap and $6.50 is left, which is split evenly: $3.25 each. Check: $18.25 + $3.25 = $21.50, and $18.25 is $15.00 more than $3.25. The quick answer of $6.50 would make the total $28.00.