# Thread: inverse variation and proportion problems!!!

1. ## inverse variation and proportion problems!!!

1) If m varies inversely as n squared (didn't know how to put little 2 subscript), and m=9 when n=2/3, find m when n=5/4.

2) Which container of ice tea is the best buy. Find this using ratio or proportion.

350g costs $3.99 600g costs$5.49
1kg costs $8.99 Thanks! 2. Originally Posted by wickedcharchar 1) If m varies inversely as n squared (didn't know how to put little 2 subscript), and m=9 when n=2/3, find m when n=5/4. Please show all steps 2) Which container of ice tea is the best buy. Find this using ratio or proportion. 350g costs$3.99
600g costs $5.49 1kg costs$8.99

Thanks!
so $\displaystyle m=\frac{k}{n^2}$ then evaluating at your two values gives

$\displaystyle 9=\frac{k}{(\frac{2}{3})^2}=\frac{k}{\frac{4}{9}}$ solveing for k gives k=4 so we get

$\displaystyle m=\frac{4}{n^2}$ using n=5/4 to evaluate we get...

$\displaystyle m=\frac{4}{(\frac{5}{4})^2}=\frac{4}{\frac{25}{16} }=\frac{64}{25}$

for the next part you want to find the unit price $\displaystyle \frac{price}{amount}$ note that the last one is in kg 1kg=1000g

So divide the price by how much for each one and pick the smallest value.