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Ashley and Castel each improved their yards by planting daylilies and ornamental grass. They

bought their supplies from the same store. Ashley spent $118 on 2 daylilies and 14 bunches of

ornamental grass. Castel spent $98 on 14 daylilies and 7 bunches of ornamental grass. What is the

of one daylily and the cost of one bunch of ornamental grass? Also could you show work

Ashley and Castel each improved their yards by planting daylilies and ornamental grass They bought their supplies from the same store Ashley spent 118 on

Answer :

Each daylily cost $3 and one bunch of ornamental grass cost $8.

Build two equation's: (Let 'd' be daylilies, 'o' be ornamental grass)

$118 on 2 daylilies and 14 bunches of ornamental grass.

  • 2d + 14o = 118

$98 on 14 daylilies and 7 bunches of ornamental grass.

  • 14d + 7o = 98

Make d subject for first equation.

2d + 14o = 118

2d = 118 - 14o

d = (118 - 14o)/2

d = 59 - 7o

Insert this into second equation.

14(59 - 7o) + 7o = 98

826 - 98o + 7o = 98

-91o = -728

o = 8

Find value of d:

d = 59 - 7o

d = 59 - 7(8)

d = 3

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Rewritten by : Barada

Answer:

Cost of one daylily = $3

Cost of one bunch of ornamental grass = $8

Step-by-step explanation:

Define the variables:

  • Let d = cost of one daylily (in dollars)
  • Let g = cost of one bunch of ornamental grass (in dollars)

Given information:

  • $118 = 2 daylilies and 14 bunches of ornamental grass
  • $98 = 14 daylilies and 7 bunches of ornamental grass

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}2d+14g=118\\14d+7g=98 \end{cases}[/tex]

Multiply the second equation by 2:

[tex]\implies 2(14d+7g)=2(98)[/tex]

[tex]\implies 28d+14g=196[/tex]

Subtract the first equation from this equation to eliminate the variable g:

[tex]\begin{array}{r r r}28d & +14g = & 196\\- \quad \quad2d & +14g = & 118\\\cline{1-3}26d & = & 78\end{array}[/tex]

Solve for d:

[tex]\implies 26d=78[/tex]

[tex]\implies d=3[/tex]

Substitute the found value of d into one of the equations and solve for g:

[tex]\implies 2d+14g=118[/tex]

[tex]\implies 2(3)+14g=118[/tex]

[tex]\implies 6+14g=118[/tex]

[tex]\implies 14g=112[/tex]

[tex]\implies g=8[/tex]

Therefore, the cost of one of each plant is:

  • Cost of one daylily = $3
  • Cost of one bunch of ornamental grass = $8

Learn more about system of equations here:

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