1990 AMC 8 Problem 24
Attempt Problem 24 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
Three triangles and a diamond balance nine dots. Also, one triangle balances a diamond and a dot. How many dots will balance two diamonds?
Answer: C
Small hint:
Let a triangle weigh , a diamond , and a dot ; write the two balance conditions as equations
Big hint:
From and , substitute to solve for , then double it
Solution:
Let a triangle, diamond, and dot weigh , , and . The conditions give and .
Substituting, , so and . Then two diamonds weigh dots.
Thus, the correct answer is C .
Problem 24 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
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- 1999 AMC 8
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