Grade 4 Math Puzzle 1: Compare two expressions by their differences

A free grade 4 math puzzle that teaches Compare two expressions by their differences. Try it first — the hint and the full solution open when you are ready.

Problem 1 · Compare two expressions by their differences · 3 points

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Lena puts the same whole number in both boxes to make 84 − 5 × □ = 48 − 2 × □. What number goes in each box?

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Which side starts with more, and which side takes away more groups of the box?
How many extra groups must be taken away to close the gap between 84 and 48?

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Answer: B — 12

The left side starts 36 higher but subtracts 3 more copies of the box. So 3 copies make 36, and each box is 12. Checking: 84 − 5 × 12 = 24 and 48 − 2 × 12 = 24. The tempting 0 comes from subtracting before multiplying, which would make both sides zero; in the given expressions, 0 gives 84 and 48.

Grade 4 puzzle 1: Compare two expressions by their differences

Problem 1 · Compare two expressions by their differences · 3 points