Aperson 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

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

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

y =  -(1/3)x - 1/3(5)

Slop of the equation is -(1/3). As parallel line have same slope, substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3