# How do you solve for s in a=s-sr ?

Mar 19, 2016

$s = \frac{a}{1 - r}$

#### Explanation:

$\textcolor{b l u e}{\text{Shortcut method}}$

By inspection, write as:$\text{ } a = s \left(1 - r\right)$

Take the $\left(1 - r\right)$ to the other side

$\frac{a}{1 - r} = s$

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$\textcolor{b l u e}{\text{From first principles}}$

Note that:
$\text{ } s \times 1 = s$
$\text{ } s \times \left(- r\right) = - s r$

So for the right hand side; factor out the $s$

$\text{ } s \left(1 - r\right)$

This means everything inside the bracket is multiplied by $s$

So now we have

$\text{ } a = s \left(1 - r\right)$

Divide both sides by $\left(1 - r\right)$ giving

$\text{ "a/(1-r)" "=" } s \times \frac{1 - r}{1 - r}$

But $\frac{1 - r}{1 - r} = 1$ so we now have

$\text{ "a/(1-r)" "=" } s \times 1$

But $s \times 1 = s$ so we have

$\text{ } \frac{a}{1 - r} = s$

Swap sides

$\text{ } s = \frac{a}{1 - r}$