Answer :
The problem presented asks for a system of linear equations to find the cost of peonies and geraniums from two separate purchases. The first equation from the purchases is 4P + 9G = $190, and the second is 5P + 6G = $185, with P representing the cost of a peony and G the cost of a geranium.
The question involves setting up a system of linear equations to determine the cost of individual plants based on the total cost of different combinations purchased by two landscapers. Let's denote the cost of a peony as P and the cost of a geranium as G. The first landscaper's purchase gives us the equation 4P + 9G = $190. The second landscaper's purchase gives us the equation 5P + 6G = $185. We have a system of two linear equations with two variables.
To solve the system, one could use methods such as substitution, elimination, or matrix operations to find the values for P (cost of peony) and G (cost of geranium).
The cost of one peony is $30, and the cost of one geranium is $10, obtained by solving the system of linear equations.
How we wrote a system of linear equations to find the cost of each plant (peonies and geraniums) given the purchase details and prices.
To obtain these values, a system of linear equations is necessary.
The first equation states that 4 peonies and 9 geraniums were purchased for a total cost of $190. This equation can be represented as 4P + 9G = 190.
The second equation indicates that 5 peonies and 6 geraniums were bought for $185. This equation can be written as 5P + 6G = 185.
By solving this system of linear equations, the values of P and G can be determined, representing the cost of each plant.
The solution reveals that one peony costs $30, while one geranium costs $10.
It is important to note that these values are rounded to the nearest dollar, and they satisfy the given purchase details and prices.
Learn more about linear equations
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