1977 AMC 12 Problem 1

Attempt Problem 1 of the 1977 AMC 12 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 1977 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

If y=2xy=2x and z=2y,z=2y, then x+y+zx+y+z equals
xx
3x3x
5x5x
7x7x
9x9x
Answer: D
Concepts:substitutionalgebraic manipulation
Small hint:
Express every term in terms of xx
Big hint:
Use y=2xy=2x first to obtain z=4xz=4x
Solution:
Since y=2x,y=2x, we have z=2y=4x.z=2y=4x. Therefore x+y+z=x+2x+4x=7x.x+y+z=x+2x+4x=7x.
Therefore, the correct answer is D.
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