Question

Kali and Asanji each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Kali spent $132 on 6 daylilies and 12 bunches of ornamental grass. Asanji spent $83 on 14 daylilies and 3 bunches of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass?

Answer 1

cost of one daylily= $4

cost of one bunch= $ 9

Explanation

Step 1

Let x represents the cost of one daylily

Let y represents the cost of one bunch

then

Kali spent $132 on 6 daylilies and 12 bunches of ornamental grass.

in math terms

$132=6x+12y\text{ Equatino(1)}$

and

Asanji spent $83 on 14 daylilies and 3 bunches of ornamental grass

$83=14x+3y\text{ Equation(2)}$

Step 2

solve for x and y

multiply equation (2) by -4 and add the result to equation(1)

$\begin{gathered} 83=14x+3y\text{ Equation(2) multiplied by -4} \\ -332=-56x-12y\text{ Equation (3)} \\ \text{Now, add Eq(1) and (3)} \\ 132=6x+12y \\ -332=-56x-12y \\ \text{.}------------ \\ -200=-50x+0 \\ \text{divide both sides by -50} \\ \frac{-200}{-50}=\frac{-50x}{-50} \\ 4=x \end{gathered}$

now, to find y, replace x equation (2) and isolate y

$\begin{gathered} 83=14x+3y\text{ Equation(2)} \\ 83=14\cdot4+3y\text{ } \\ 83=56+3y \\ \text{subtract 56 in both sides} \\ 83-56=56+3y-56 \\ 27=3y \\ \text{divide both sides by 3} \\ \frac{27}{3}=\frac{3y}{3} \\ 9=y \end{gathered}$

so

cost of one daylily= $4

cost of one bunch= $ 9