2005 AMC 10A Problem 3 — Solution | LIVE by Po-Shen Loh

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2005 AMC 10A Problem 3

Attempt Problem 3 of the 2005 AMC 10A 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 2005 AMC 10A solutions, or check the answer key.

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

3.

The equations $2x + 7 = 3$ and $bx - 10 = -2$ have the same solution $x.$ What is the value of $b?$

$-8$

$-4$

$-2$

$4$

$8$

Answer: B

Concepts:linear equation substitution

Difficulty rating: 960

Solution:

From $2x + 7 = 3$ we get $x = -2.$ Substituting, $-2b - 10 = -2,$ so $-2b = 8$ and $b = -4.$

Thus, the correct answer is B.

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