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Thread: X and Y

  1. #1
    Junior Member Dragon's Avatar
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    Oct 2006
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    X and Y

    Suppose that
    x/y= 4/7
    And that y/z=14/3

    What is the value of x+y/z

    Express your answer as a common fraction.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Dragon!

    Suppose that: $\displaystyle \frac{x}{y} = \frac{4}{7}$ and $\displaystyle \frac{y}{z} = \frac{14}{3}$

    What is the value of $\displaystyle \frac{x + y}{z}$ ?

    Multiply the two equations: .$\displaystyle \frac{x}{y}\cdot\frac{y}{z}\:=\:\frac{4}{7}\cdot\f rac{14}{3}\quad\Rightarrow\quad\frac{x}{z} = \frac{8}{3}$

    So we have: .$\displaystyle \frac{x}{z} = \frac{8}{3}$ and $\displaystyle \frac{y}{z} = \frac{14}{3}$

    Add these two equations: .$\displaystyle \frac{x}{z} + \frac{y}{z} \:=\:\frac{8}{3} + \frac{14}{3}\quad\Rightarrow\quad\boxed{\frac{x+y} {z} \:=\:\frac{22}{3}}$

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