Question

9) Sumalee and Arjun each improved their yards by planting grass sod and shrubs. They

supplies from the same store. Sumalee spent $45 on 3 ft of grass sod and 5 shrubs. Arjun spent $63
on 3 ft- of grass sod and 11 shrubs. Find the cost of one ft2 of grass sod and the cost of one shrub.
A) ft of grass sod: $11, shrub: $5
B) ft2 of grass sod: $4, shrub: $4
C) ft2 of grass sod: $10, shrub: $3
D) ft2 of grass sod: $6, shrub: $5

Answer 1

System of Equations

Let's define the following variables:

x = Cost of each square ft of grass sod

y = Cost of each shrub

Sumalee spent $45 on 3 square ft of grass sod and 5 shrubs. Using our previously defined variables, we set up the first equation:

3x + 5y = 45 [1]

Arjun spent $63 on 3 square ft of grass sod and 11 shrubs, thus our second equation is:

3x + 11y = 63 [2]

We'll use the elimination method to solve the system of equations.

Taking advantage that the coefficient of x is the same on both equations, we subtract [1] from [2]:

11y - 5y = 63 - 45

Simplifying:

6y = 18

Dividing by 6:

y = 3

Substituting into [2]:

3x + 11(3) = 63

Operating:

3x + 33 = 63

Subtracting 33:

3x = 30

Dividing by 3:

x = 30/3

x = 10

Answer: C)