Respuesta :
Answer:
The cost of [tex]1 ft^2[/tex] of grass sod is $7
The cost of one piece of shrub is $9
Step-by-step explanation:
Let [tex]G[/tex] represent [tex]1 ft^2[/tex] of grass sod and [tex]S[/tex] represents one piece of shrub
Joe spent $[tex]$80[/tex] on [tex]5 ft^2[/tex] of grass sod and [tex]5[/tex] pieces of shrubs (shelves)
[tex]5G + 5S=80[/tex] [tex]eq. 1[/tex]
Lisa spent $[tex]94[/tex] on [tex]7 ft^2[/tex] of grass sod and [tex]5[/tex] pieces of shrubs (Chevy)
[tex]7G + 5S=94[/tex] [tex]eq. 2[/tex]
from [tex]eq. 1[/tex]
[tex]5G=80 - 5S[/tex]
[tex]G=\frac{80-5S}{5}[/tex] [tex]eq. 3[/tex]
Now put the [tex]eq. 3[/tex] into [tex]eq. 2[/tex]
[tex]7G + 5S=94[/tex]
[tex]7(\frac{80-5S}{5}) + 5S=94[/tex]
[tex]\frac{560-35S}{5} + 5S=94[/tex]
[tex]\frac{560-35S + 5(5S)}{5} =94[/tex]
[tex]{560-35S + 25S =94*5[/tex]
[tex]560-10S =470[/tex]
[tex]560-470 =10S[/tex]
[tex]90 =10S[/tex]
[tex]S= 90/10 = 9[/tex]
The cost of one piece of shrub is $9
Now put the value of [tex]S[/tex] into [tex]eq. 3[/tex] to get value of [tex]G[/tex]
[tex]G=\frac{80-5S}{5}[/tex]
[tex]G=\frac{80-5(9)}{5}[/tex]
[tex]G=\frac{80-45}{5}[/tex]
[tex]G=\frac{35}{5}[/tex]
[tex]G=7[/tex]
The cost of [tex]1 ft^2[/tex] of grass sod is $7
