Question

Cody and Matt are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs. Cody sold 2 bags of windflower bulbs and 5 bags of daffodil bulbs for a total of $105. Matt sold 4 bags of windflower bulbs and 3 bags of daffodil bulbs for a total of $91. What is the cost each of one bag of windflower bulbs and one bag of daffodil bags?

Answer 1

Given

Cody sold 2 bags of windflower bulbs and 5 bags of daffodil bulbs for a total of $105.

Matt sold 4 bags of windflower bulbs and 3 bags of daffodil bulbs for a total of $91.

Solution

Step 1

Let's bags of windflower be represented by W

Let's bags of daffodil bulbs be represented by D

`\begin{gathered} \text{For Cody} \\ 2w+5d=105\ldots\text{Equation(i)} \\ for\text{ Matt} \\ 4w+3d=91\ldots\text{Equation (i}i) \end{gathered}`

Step 2

Using Substitution method

`\begin{gathered} 2w+5d=105\ldots\text{Equation(i)} \\ 4w+3d=91\ldots\text{Equation (i}i) \\ \text{From equation (i) make w the subject of the formula} \\ 2w+5d=105\ldots\text{Equation(i)} \\ 2w=105-5d \\ \text{divide both sides by 2} \\ w=(105-5d)/(2) \end{gathered}`

Step 3

We can now substitute to Equation(ii)

`\begin{gathered} 4((105-5d)/(2))+3d=91 \\ \\ 2(105-5d)+3d=91 \\ 210-10d+3d=91 \\ 210-7d=91 \\ \text{collect the like terms} \\ -7d=91-210 \\ -7d=-119 \\ \text{Divide both sides by -7d} \\ -(7d)/(7)=-(119)/(7) \\ \\ d=17 \end{gathered}`

Step 4

we can substitute for d in either equation (i) or (ii) to find w

`\begin{gathered} \text{Equation (i)} \\ 2w+5d=105 \\ 2w+5(17)=105 \\ 2w+85=105 \\ \text{collect the like terms} \\ 2w=105-85 \\ 2w=20 \\ \text{Divide bot sides by 2} \\ (2w)/(2)=(20)/(2) \\ w=10 \end{gathered}`

The final answer

one bag of windflower bulbs =$10

one bag of daffodil bag= $17