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.

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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

Solve

2x + 7 = 3

for

x

first

Substitute that value of

x

into

bx - 10 = -2

and solve for

b

From

2x + 7 = 3

we get

x = -2.

Substituting,

-2b - 10 = -2,

-2b = 8

and

b = -4.

Thus, the correct answer is B.

Problem 3 in other years