# How do you use cross products to solve 2/t=5/(t-6)?

May 14, 2018

$t = - 4$

#### Explanation:

Cross multiply the denominator with numerator like:

$\frac{2}{t} = \frac{5}{t - 6}$

$2 \times \left(t - 6\right) = 5 \times t$

$2 t - 12 = 5 t$

Add $12$ both sides:
$2 t - 12 + 12$ = 5t+12

$2 t \cancel{- 12 + 12}$ = 5t+12

$2 t = 5 t + 12$
$2 t - 5 t = 12$ -----> making $t$ the subject by subtracting $- 5 t$ both sides:

$- 3 t = 12$

$t = - \frac{12}{3}$

$t = - 4$

May 14, 2018

$t = - 4$

#### Explanation:

$\text{using the method of "color(blue)"cross-products}$

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$\Rightarrow 5 t = 2 \left(t - 6\right)$

$\Rightarrow 5 t = 2 t - 12$

$\text{subtract "2t" from both sides}$

$5 t - 2 t = \cancel{2 t} \cancel{- 2 t} - 12$

$\Rightarrow 3 t = - 12$

$\text{divide both sides by 3}$

$\frac{\cancel{3} t}{\cancel{3}} = \frac{- 12}{3}$

$\Rightarrow t = - 4$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if both sides are equal then it is the solution.

$\text{left } = \frac{2}{- 4} = - \frac{1}{2}$

$\text{right } = \frac{5}{- 4 - 6} = \frac{5}{- 10} = - \frac{1}{2}$

$\Rightarrow t = - 4 \text{ is the solution}$