Word problem on total cost of packages

Question

Julia sold 4 bags of windflowers and 6 packages of crocus bulbs for a total of $136. Stefan sold 12 bags of windflowers and 12 packages of crocus bulbs for a total of $312. What is the cost of one bag of windflower bulbs and on package of crocus bulbs

Answer 1

Hello Abi!

 

 

Do you need the combined cost of one bag of windflower bulbs and one package of crocus bulbs or you need the cost of each? 

 

If you need the combined cost, here is the solution:

 

 

Let w = cost of a bag of windflowers

      c = cost of a bag of crocus bulbs

 

 

       4w + 6c = 136     (irrelevant)

 

   (12w + 12c = 312) /12            Divide the whole equation by 12

 

       w + c = $26

 

2) If you need the cost of each, then we will use this solution:

 

         4w + 6c = 136 (-2)                    Multiply this whole equation by -2 to eliminate c

        12w + 12c = 312

 

 

         -8w - 12c = -272

         12w + 12c = 312                      Add the two equations.

 

The sum would be:

 

        4w = 40;     Divide both sides by 4

        w   = $10

   

 

Solve c in terms of w.

 

 

        4w + 6c = 136

      4 (10) + 6c  = 136

          40 + 6c = 136

 

          6c = 136 -40

          6c = 96

            c = 96/6

             c = $16

 

 

Hope that helps.