A person wishes to mix coffee worth ​$9 per lb with coffee worth ​$3 per lb to get 150 lb of a mixture worth ​$5 per lb. How many pounds of the ​$9 and the ​$3 coffees will be​ needed

Answer:50 lb of $9 coffee and 100 lb of $3 coffee  Step-by-step explanation:   Let x = the pounds of $9 coffee. Then 150 - x = the pounds of $3 coffee. We can calculate the value of the coffee in each mixture.      x lb × $9/lb + (150 -x ) lb × $3/lb = 150 lb × $5/lb               9x        +       3(150 - x)        = 750 Distribute the 3         9x + 450 -  3x = 750 Combine like terms          450 + 6x = 750 Subtract 450 from each side      6x = 300 Divide each side by 6                    x =   50 lb of $9 coffee                                               150 - x  = 100 lb of $3 coffee The person must mix 50 lb of $9/lb coffee with 100 lb of $3/lb coffee to get 150 lb of $5/lb coffee. Check: 50 × 9 + 100 × 3 = 750  450   +    300   = 750                 750    = 750