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Thread: finding t?

  1. #1
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    finding t?

    hey guys, i need to know how to solve this problem..

    7t-2/5 = t+4/3

    find t ?

    btw they are two fractions.

    if anyone can give me the run down from start to finish that would be excellent.

    jvignacio.
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  2. #2
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    Hello, jvignacio

    Solve: .$\displaystyle \frac{7t-2}{5}\;=\;\frac{t+4}{3}$

    Multiply both sides by the LCD, 15:

    . . $\displaystyle 15\cdot\frac{7t-2}{5} \;=\;15\cdot\frac{t+4}{3}\quad\Rightarrow\quad 3(7t-2) \;=\;5(t+4)$

    . . $\displaystyle 21t - 6 \:=\:5t+20 \quad\Rightarrow\quad 16t \:=\:26$


    Therefore: .$\displaystyle t \:=\:\frac{26}{16} \:=\:\boxed{\frac{13}{8}}$

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, jvignacio


    Multiply both sides by the LCD, 15:

    . . $\displaystyle 15\cdot\frac{7t-2}{5} \;=\;15\cdot\frac{t+4}{3}\quad\Rightarrow\quad 3(7t-2) \;=\;5(t+4)$

    . . $\displaystyle 21t - 6 \:=\:5t+20 \quad\Rightarrow\quad 16t \:=\:26$


    Therefore: .$\displaystyle t \:=\:\frac{26}{16} \:=\:\boxed{\frac{13}{8}}$
    hey thank you! quick question - how did you get this...


    . . $\displaystyle 3(7t-2) \;=\;5(t+4)$

    from


    $\displaystyle 15\cdot\frac{7t-2}{5} \;=\;15\cdot\frac{t+4}{3}$
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  4. #4
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    Hello again, jvignacio!

    Quick question

    How did you get this: .$\displaystyle 3(7t-2) \;=\;5(t+4)$

    from: . $\displaystyle 15\cdot\frac{7t-2}{5} \;=\;15\cdot\frac{t+4}{3}$

    Just reduce: .$\displaystyle \not{1}\!\!\!\!\not{5}^3\cdot\frac{7t-2}{\not{5}} \;=\;\not{1}\!\!\!\!\not{5}^5\cdot\frac{t+4}{\not{ 3}} \quad\Rightarrow\quad 3(7t-2)\:=\:5(t+4)$

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