Question

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

Answer 1

Answer:

cost 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:

$\begin{cases}2d+14g=118\\14d+7g=98 \end{cases}$

Multiply the second equation by 2:

$\implies 2(14d+7g)=2(98)$

$\implies 28d+14g=196$

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

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

Solve for d:

$\implies 26d=78$

$\implies d=3$

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

$\implies 2d+14g=118$

$\implies 2(3)+14g=118$

$\implies 6+14g=118$

$\implies 14g=112$

$\implies g=8$

Therefore, the cost of one of each plant is:

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

Learn more about system of equations here:

brainly.com/question/27930827

Answer 2

Answer: Each daylily cost $3 and each ornamental glass 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