1982 AMC 12 Problem 2

Attempt Problem 2 of the 1982 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 1982 AMC 12 solutions, or check the answer key.

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

2.

If a number eight times as large as xx is increased by two, then one fourth of the result equals
2x+122x+\frac12
x+12x+\frac12
2x+22x+2
2x+42x+4
2x+162x+16
Answer: A
Concepts:order of operationsalgebraic manipulation
Small hint:
Translate the first two operations before dividing
Big hint:
Simplify 8x+24\frac{8x+2}{4} term by term
Solution:
Eight times x,x, increased by two, is 8x+2.8x+2. One fourth is 8x+24=2x+12.\frac{8x+2}{4}=2x+\frac12.
Therefore, the correct answer is A.
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