# In order to determine the slant height of several pyramids, Marjorie used the surface area formula, S = 1/2 pt + b for the slant height, t. What equation would be the correct transformation of the surface area formula for t?

Jan 5, 2018

$t = \frac{2 \left(S - b\right)}{p}$

#### Explanation:

So we need to solve the equation for $t$.

First, subtract $b$ from both sides.
$S \textcolor{red}{- b} = \frac{1}{2} p t \textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{+ b}} \cancel{\textcolor{red}{- b}}}$
$S - b = \frac{1}{2} p t$

Then, multiply both sides by $2$.
$\textcolor{red}{2} \times \left(S - b\right) = \textcolor{g r e e n}{\cancel{\textcolor{red}{2 \times}} \cancel{\textcolor{b l a c k}{\frac{1}{2}}}} p t$
$2 \left(S - b\right) = p t$

Finally, divide both sides by $p$.
$2 \left(S - b\right) \textcolor{red}{\div i \mathrm{de} p} = \textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{p}}} t \textcolor{g r e e n}{\cancel{\textcolor{red}{\div i \mathrm{de} p}}}$
$\frac{2 \left(S - b\right)}{p} = t$