Question

Arjun and Chelsea each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Arjun spent $114 on 7 daylilies and 12 bunches of ornamental grass. Chelsea spent $84 on 8 daylilies and 6 bunches of ornamental grass. Find the cost of one daylily and the cost of one bunch of ornamental grass.

Answer 1

We have a problem about a system of equations

x= cost per one daylily

y=cost per one bunch

the equation for Arjun

7 daylilies

12 bunches

total cost 114

7x+12y=114

the equation for Chelsea

8 daylilies

6 bunches

total cost 84

8x+6y=84

the system of equations we have is

7x+12y=114

8x+6y=84

In order to solve the system, we will multiplicate the second equation by -2

`-2(8x+6y=84)=-16x-12y=-168`

then we will sum the first equation with the equation above

`-16x+7x-12y+12y=-168+114`

then we sum similar terms

`-9x=-54`

then we isolate x

`\begin{gathered} x=(-54)/(-9) \\ x=6 \end{gathered}`

then we will substitute the value of x in the first equation in order to find y

`\begin{gathered} 7(6)+12y=114 \\ 42+12y=114 \\ 12y=114-42 \\ 12y=72 \\ y=(72)/(12) \\ y=6 \end{gathered}`

the solution is

cost of one daylily =x=6

cost of one bunch =y=6