What is the cost of one bag of windflower bulbs and one bag of daffodil bulbs?

Question

Amy and Molly are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs. Amy sold 14 bags of windflower bulbs and 4 bags of daffodil bulbs for a total of $150. Molly sold 7 bags of windflower bulbs and 3 bags of daffodil bulbs for a total of $88. What is the cost each of one bag of windflower bulbs and one bag of daffodil bulbs?

Answer 1

Hi Sonseeahray, this is what's called a mixture problem. Let's let W = windflower bulbs, and D = daffodil bulbs. We know that number of bags multiplied by the price per bag equals total cost. Number* $ price = $ total. So we set up equations to show this with the numbers given in the problem!

 

Amy sold: 14W + 4D = $150

Molly sold: 7W + 3D = $88

 

Solve this system of equations using whatever method you like to get values for both W and D. I'll solve for D and leave you to finish the rest. Multiply Molly's equation (equation 2) by 2. 

 

14W + 4D = 150

14W + 6D = 176

 

Subtract equation 2 from equation 1:

 

   14W + 4D = 150
- [14W + 6D = 176]

              -2D = -26

                 D = 13

 

This means the cost of one bag of daffodil bulbs is $13. Now, substitute the value of D back into any equation to solve for W. Hope that helps!