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Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

Three straight lines, $l_1$ , $l_2$ and $l_3$ , have slopes $\dfrac{1}{2}$ , $\dfrac{1}{3}$ and $\dfrac{1}{4}$ , respectively. All three lines have the same $y$ -intercept. If the sum of the $x$ -intercepts of the three lines is $36$ , then the $y$ -intercept is

(A) $\dfrac{-13}{12}$ (B) $\dfrac{-12}{13}$ (C) $-4$ (D) $4$ (E) $-9$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.