#### Answer

To feed 200 people we need: 35.7 lb of meat, 50 lb of potatoes, and 21.4 lb of carrots.

#### Work Step by Step

We know that 25 lb of meat fed 140 people. To find out how much meat is needed to feed 200 people, we set up a proportion:
$\displaystyle \frac{25~lb}{140~people}=\frac{x}{200~people}$
Cross-multiply:
$25*200=x*140$
$5000=x*140$
$x=5000/140$
$x\approx35.7$ lb of meat
We use the same method with 35 lb of potatoes:
$\displaystyle \frac{35~lb}{140~people}=\frac{x}{200~people}$
Cross-multiply:
$35*200=x*140$
$7000=x*140$
$x=7000/140$
$x\approx 50$ lb of potatoes
We also use the same method with 15 lb of carrots:
$\displaystyle \frac{15~lb}{140~people}=\frac{x}{200~people}$
Cross-multiply:
$15*200=x*140$
$3000=x*140$
$x=3000/140$
$x\approx 21.4$ lb of carrots
So to feed 200 people we need: 35.7 lb of meat, 50 lb of potatoes, and 21.4 lb of carrots.