Difference between revisions of "2006 AMC 12B Problems/Problem 8"

Revision as of 17:51, 27 March 2015

The lines $x = \frac 14y + a$ and $y = \frac 14x + b$ intersect at the point $(1,2)$ . What is $a + b$ ?

$\text {(A) } 0 \qquad \text {(B) } \frac 34 \qquad \text {(C) } 1 \qquad \text {(D) } 2 \qquad \text {(E) } \frac 94$

$4x-4a=y$

$4x-4a=\frac{1}{4}x+b$

$4*1-4a=\frac{1}{4}*1+b=2$

$a=\frac{1}{2}$

$b=\frac{7}{4}$

$a+b=\frac{9}{4} \Rightarrow \text{(E)}$

2006 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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 == Problem ==
-The lines <math>x = \frac 14y + a</math> and <math>y = \frac 14x + b</math> intersect at the point <math>(1,2)</math>.  What is <math>a + b</math>?
+<!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>The lines <math>x = \frac 14y + a</math> and <math>y = \frac 14x + b</math> intersect at the point <math>(1,2)</math>.  What is <math>a + b</math>?<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude>
 <math>