Originally Posted by

**fsiwaju** Hello,

**The quantities of ***S *and *T *are positive and related by the equation *S= k/T *where *k *is a constant. If the value of *S *increases by 50%, then the value of *T *decreases by what percent?

a) 25%

b) 33 1/3 %

c) 50%

d) 66 2/3 %

e) 75%

If $\displaystyle S$ and $\displaystyle T$ are positive and $\displaystyle S=\frac{k}{T}$ , then $\displaystyle k$ must be a positive constant.

So, let's assign positive numerical values to $\displaystyle S$, $\displaystyle T$, and $\displaystyle k$ such that $\displaystyle S=\frac{k}{T}$.

For example, let $\displaystyle S=10$, $\displaystyle k=1000$ and $\displaystyle T=100$.

These values work for $\displaystyle S=\frac{k}{T}$.

Then,

$\displaystyle 1.5S=\frac{k}{T_*} \implies 1.5\left(10\right)=\frac{1000}{T_*} \implies T_* = \frac{1000}{15} = 66.\overline{66} $

$\displaystyle T=100$ and $\displaystyle T_*=66.\overline{66}$, which is a decrease of $\displaystyle 33.\overline{33}\%$.