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A jar contains red and blue marbles in the ratio 2 to 3. After 10 more red marbles are added to the jar and no marbles are removed, the ratio of red to blue marbles becomes 4 to 3. How many marbles were in the jar originally?
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Correct answer
C
Let red = 2k and blue = 3k. Blue is unchanged and red becomes 2k + 10, so (2k + 10)/3k = 4/3. Cross-multiplying gives 3(2k + 10) = 4(3k), so 6k + 30 = 12k, giving 6k = 30 and k = 5. Then red = 10, blue = 15, and the original total = 5k = 25. So the answer is C.
You can also anchor on the unchanged blue count: blue is 3 parts in both ratios, so 3 parts = 15 means 1 part = 5, giving red = 10 and total = 25.
The question asks for the original total, not the new red count of 20 (choice B) or the new total of 35 (choice D). Choice A, 15, reports the blue count, and choice E, 40, doubles the new red count of 20.
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