A store sells almonds for $6 per pound, cashews for $5 per pound and peanuts for $2 per pound. One week the manager decides to prepare 100 1-pound packages of nuts by mixing the peanuts, cashews and almonds. Each package will be sold for $4. The mixture is to produce the same revenue as selling the nuts separately.
Write down the system of equations which captures this information and use Gaussian elimination to reduce it. Write down at least 3 solutions which make sense to this system.

Question

A store sells almonds for $6 per pound, cashews for $5 per pound and peanuts for $2 per pound. One week the manager decides to prepare 100 1-pound packages of nuts by mixing the peanuts, cashews and almonds. Each package will be sold for $4. The mixture is to produce the same revenue as selling the nuts separately.  
Write down the system of equations which captures this information and use Gaussian elimination to reduce it. Write down at least 3 solutions which make sense to this system.