Grade 6 Math Puzzle 4: Compare shares of an unchanged total

A free grade 6 math puzzle that teaches Compare shares of an unchanged total. Try it first — the hint and the full solution open when you are ready.

Problem 4 · Compare shares of an unchanged total · 4 points

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Lina and Mo have stickers in the ratio 3 : 5. Lina gives Mo 3 stickers, and now Mo has twice as many as Lina. How many stickers did Lina have at first?

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The gift changes each person's share, but not their combined total. Compare Lina's share before and after.
Lina starts with 3/8 of the total and ends with 1/3 of it. What fraction of the total did she give away?

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Answer: A — 27

Lina gives away 3/8 − 1/3 = 1/24 of the unchanged total. Since that is 3 stickers, the total is 72. Lina started with 3/8 of 72, or 27 stickers. The tempting 24 is how many she has after giving away 3.

Grade 6 puzzle 4: Compare shares of an unchanged total

Problem 4 · Compare shares of an unchanged total · 4 points