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Answer :
The cost of one ft² of sod is $2 and the cost of one geranium is $9.
What are the linear equations that represent the question?
9s + 2g = 36 equation 1
9s + 5g = 63 equation 2
What is the cost of one feet of sod and geranium?
Subtract equation 1 from equation 2:
3g = 27
g = 27 / 3
g = $9
Substitute for g in equation 1
9s + (2 x 9) = 36
9s + 18 = 36
9s = 36 - 18
9s = 18
s = 18 / 9
s = $2
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Final answer:
The cost of one ft² of sod is $2 and the cost of one geranium is $9. This was determined by solving a system of linear equations that represent the purchases of Eugene and Shanice.
Explanation:
To solve for the cost of one ft² of sod (s) and the cost of one geranium (g), we can set up two linear equations based on the information provided:
Eugene's purchase: 36 = 9s + 2g
Shanice's purchase: 63 = 9s + 5g
Solving this system of equations:
Multiplying Eugene's equation by -1 gives us: -36 = -9s - 2g
Adding the two equations together to eliminate 's' yields: 27 = 3g
Dividing by 3 gives the cost of one geranium: g = 9
Substitute g into Eugene's equation: 36 = 9s + 2(9)
Solve for s, we get: 36 = 9s + 18
Subtract 18 from both sides: 18 = 9s
Divide by 9, we find the cost of one ft² of sod: s = 2
Therefore, one ft² of sod costs $2 and one geranium costs $9.
