How much redwood does Travis have to buy?

Question

Redwood         $2.50               $2.30

 

Plywood           $1.20               $1.00

 

In store , he would pay $4530, and in store B it would be $4100.

Answer 1

   Let R equal amount of redwood he needs

   Let P equal amount of plywood he needs

 

For Store A:

   $4530  =  $2.50 R  +  $1.20 P       (1)

 

For Store B:

   $4100 =  $2.30 R +  $1.00 P         (2)

 

You now have two equations with two unknowns.  We need to find the value of R.

 

Rewriting expression (2):

    P  =  4100  -  2.3 R

 

Substitute this for P into expression (1):

   4530  =  2.5 R  +  1.2 (4100 - 2.3 R)

            =  2.5 R  +  4920  -  2.76 R  =  4920  - 0.26 R

 

   0.26 R  =  4920  -  4530  =  390

 

          R   =  390 / 0.26  = 1500

 

As a check, we can find the value of P:

      P  =  4100  -  2.3 R   

          =  4100  -  2.3 (1500) 

          =  4100  -  3450    =   650