1. ## 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.

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

3. Originally Posted by Soroban
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

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

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