#### Answer

36lb of meat, 50 lb of potatoes and 21lb of carrots are needed.

#### Work Step by Step

1. Get the factor to increase the mass of each ingredient by can be determined by $200\div140=\frac{10}{7}$
2. The mass of each ingredient required to serve 200 people is determined by multiplying the factor with the original individual mass of each ingredient.
Mass of meat:$\frac{10}{7}\times25=35.714...\approx36$
Mass of potatoes:$\frac{10}{7}\times35=50$
Mass of carrots:$\frac{10}{7}\times15=21.428...\approx21$