Joe and Emily each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Joe spent $62 on 1 ft² of grass sod and 6 geraniums. Emily spent $42 on 1 ft² of grass sod and 4 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?

Question

28-09-2023
Mathematics

High School

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Joe and Emily each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Joe spent $62 on 1 ft² of grass sod and 6 geraniums. Emily spent $42 on 1 ft² of grass sod and 4 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?

Answer :

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JacobWilliamsJr JacobWilliamsJr · Answer 1 · 2025-03-30T06:47:04-04:00

The cost of one ft2 of grass sod is $22, and the cost of one geranium is $10. This was found by solving a system of equations derived from Joe's purchase of sod and 6 geraniums for $62, and Emily's purchase of sod and 4 geraniums for $42.

Joe and Emily are purchasing supplies for their yard work. Each of them buys 1 ft2 of grass sod and some geraniums, spending $62 and $42 respectively. To determine the cost of one ft2 of grass sod and one geranium, we can set up a system of equations based on their purchases:

Let x represent the cost of one ft2 of grass sod.
Let y represent the cost of one geranium.

The system of equations based on their spending would be:

x + 6y = 62 (Joe's purchase)
x + 4y = 42 (Emily's purchase)

To solve the system, first subtract the second equation from the first to find the cost of two geraniums. That will give you 2y = 20, which means each geranium costs $10.

Then substitute the value of y back into either equation to find the cost of grass sod x, which will be $22.