Please work this problem showing all steps so that I can understand it.

Consider a simple society composed of three people (industries) - a farmer who grows all the food, a tailor who makes all the clothing, and a carpenter who builds all the housing. Assume that each person sells to and buys from a central pool and that everything is consumed. The proportion of each of the commodities consumed by each person is given in the table. Food Clothing Housing Farmer 0.20 Tailor 0.60 Carpenter 0.20 This is a Leontief model. Find prices such that for each industry total expenditures equal total income