Jennifer and Natalie each improved their yards by planting sod and geraniums. They bought their supplies from the same store. Jennifer spent $99 on 9 ft2 of sod, s𝑠, and 9 geraniums, g𝑔. Natalie spent $82 on 10 ft2 of sod and 3 geraniums. Write equations to represent the scenario. Then, find the cost of one ft2 of sod and the cost of one geranium. Jennifer: Natalie: Square Feet of Sod: $ Geranium: $
Question
Jennifer and Natalie each improved their yards by planting sod and geraniums. They bought their supplies from the same store. Jennifer spent 82 on 10 ft2 of sod and 3 geraniums. Write equations to represent the scenario. Then, find the cost of one ft2 of sod and the cost of one geranium. Jennifer: Natalie: Square Feet of Sod:
Solution
Let's denote the cost of one square foot of sod as s and the cost of one geranium as g.
From the problem, we can write two equations based on the information given:
For Jennifer: 9s + 9g = 82
Now we have a system of two equations, and we can solve it step by step.
First, let's multiply the second equation by 3 to make the coefficients of g the same in both equations:
30s + 9g = $246
Now, subtract the first equation (Jennifer's) from this new equation:
30s + 9g - (9s + 9g) = 99 21s = $147
Now, divide both sides by 21 to solve for s:
s = 7
Substitute s = $7 into the first equation (Jennifer's):
9*7 + 9g = 99 9g = 36
Now, divide both sides by 9 to solve for g:
g = 4
So, the cost of one square foot of sod is 4.
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