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The Book and the Bookmark (illustration)
FILE No.121Unsolved

The Book and the Bookmark

Difficulty ★☆☆about 5 minLogic PuzzleEquationsChecking the math
A book and a bookmark cost 2,200 yen together. The book costs 2,000 yen more than the bookmark. How much is the bookmark?

Case Record

You bought a book and a bookmark for 2,200 yen in total. The book costs 2,000 yen more than the bookmark.

Your question

How much is the bookmark?

Case Files

Diagram

The book and the bookmarkItemDetailTogether2,200 yenThe book costs2,000 yen moreBookmark??
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

Let the bookmark be □ yen and write an equation.

Open hint 2

The book's price is □ plus how many yen?

Open hint 3

Think of the "total" and the "difference" separately.

Solve It

Your question

How much is the bookmark?

Choose the answer closest to the truth.

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The Truth

100 yen

The answer is "100 yen."

Let the bookmark be □ yen. Then the book is □ + 2,000 yen. The total is □ + □ + 2,000 = 2,200 yen, so □ = 100 yen.

If it were 200 yen, the book would be 2,200 yen, and the total would come to 2,400 yen.

Let the bookmark cost □ yenFormulaWorkingBook□ + 2,000Total□ + (□ + 2,000) = 2,200□ × 22,200 − 2,000 = 200Bookmark100 yen (book: 2,100 yen)
Diagram of the solution

Key Points

  • Do not confuse "difference" with "total"
  • Set up an equation and check it
  • Always verify an answer that comes from intuition

Why people get fooled

Because it is easy to subtract quickly: "2,200 minus 2,000 is 200."

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