The manager of a concert venue is adding up the proceeds from a friday night show. tickets sold for $8, $10, and $12 depending on where the seats were. twice as many $8 seats were sold as $10, and 10 more $12 seats were sold than $10. the total proceeds were $3,122. how many of each type of ticket were sold?

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?